1. M ATHEMATICAL P UZZLE S TARTERS Taken from http://7puzzleblog.com/http://7puzzleblog.com/ Random Puzzle Blue – Easy Orange – Medium Green – Hard Yellow – Solid Click to go to a random puzzle

2. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the answer of 7 by using the formula (a x b) ± c, where a b c are three unique digits from 2-9. If (5 x 2) – 3 = 7, list the other FOUR ways of making 7, keeping to the above rules.

3. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using the numbers 3 5 5 once each, with + – x ÷available, which FOUR numbers from the following list are NOT mathematically possible to make: 1 4 7 10 13 15 18 20 22 25 28 30

4. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem List the THREE ways of making 36 when adding together six unique digits from 1-9?

5. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of each of these 4-number calculations, when working one step at a time from Left to Right (and no brackets allowed), is 28: 6 ? 5 ? 9 ? 8 = 28 8 ? 5 ? 5 ? 7 = 28 8 ? 6 ? 8 ? 2 = 28 6 ? 7 ? 2 ? 2 = 28

6. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of each of these 4-number calculations, when working one step at a time from Left to Right (with no brackets), is 21 every time: 6 ? 5 ? 2 ? 1 = 21 4 ? 3 ? 1 ? 3 = 21 7 ? 2 ? 3 ? 2 = 21

7. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 12 letters shown below with 0, 1, 2, 2, 3, 3, 4, 6, 6, 7, 9, 9 so all three lines work out: A + B = 6 = C - D E + F = 18 = G x H I + J = 3 = K ÷ L

8. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You have the same starting number and final answer, both 32, with lots of arithmetical steps in between, but the 10th step is missing! What should it be? Start with the number 32, then: -5 ÷9 +4 x3 -3 ÷2 x5 -5 ÷2 ? x2 +4 ÷3 x2 = 32

9. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You have the same starting number and final answer, both 22, with lots of arithmetical steps in between, but the 10th and final step is missing! What should it be? Start with the number 22, then: +2 ÷6 x4 -3 x2 +4 ÷5 +5 x2 ? = 22

10. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Apart from 9+8+7+1, list the FIVE other ways of making 25 when adding together 4 UNIQUE digits from 1-9?

11. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Which is the ONLY way of making 16 when adding together 5 unique digits from 1-9?

12. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Playing a typical game of darts on a normal dartboard, you need 92 to win the game, but have just TWO darts left. Apart from TREBLE 20 DOUBLE 16, which are the other TWO ways you can end the match?

13. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle Problem 1 Add together: the months in six years the days in February (non-leap year) the minutes in three hours the seconds in five minutes What is your total answer?

14. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using the numbers 3 5 6 once each, and with + – x ÷ available, which target answers from 1-9 are NOT mathematically possible to achieve?

15. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Analyse the first three sets of numbers to find the value of ? in the fourth set: 6-8-5 = 9 / 6-7-8 = 5 / 7-8-9 = 6 / 7-1-3 = ?

16. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Which is the ONLY way of making 39 when adding together 6 unique digits from 1-9?

17. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem After analysing the first three sets of numbers, find the value of ? in the fourth set: 1-2-3 = 5 / 2-3-4 = 8 / 4-5-6 = 14 / 10-11-12 = ?

18. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem What is the next number in the sequence, and why? 283 284 142 71 72 36 18 9 ?

19. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You have been given a starting number and must arrive at the same final answer, both 18, with lots of arithmetical steps in between, but the 9th and penultimate step is missing! What should it be? Starting at 18: ÷2 +3 -8 x6 +4 -3 ÷5 x2 ? x3 = 18

20. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle Problem 1 Insert + – x or ÷ each time you see ? so the result of each of the 4-number calculations shown below is 38 when working one step at a time from Left to Right (no brackets): 7 ? 8 ? 9 ? 9 = 38 2 ? 9 ? 3 ? 5 = 38 6 ? 4 ? 9 ? 2 = 38 8 ? 2 ? 8 ? 6 = 38

21. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? below, so the result of this 4-number calculation is 29. You must work one step at a time from Left to Right (and no brackets allowed). 2 ? 3 ? 5 ? 4 = 29

22. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem One way of arriving at 31 by adding 5 unique digits is 9+8+7+6+1. Can you find the other FOUR ways of making 31 when adding together 5 unique digits from 1-9?

23. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You have to make 9 when adding together either 2 or 3 unique digits from 1-9. There are just SEVEN ways to do this, can you list them?

24. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle Problem 2 Each flavoured Gem represents a number from 1 to 9. Can you discover the value of each Gem, then find the total of the 5th row? LEMON + PURPLE + WHITE = 15 LEMON + LEMON + WHITE = 16 PURPLE + LEMON + PURPLE = 10 WHITE + WHITE + WHITE = 24 WHITE + WHITE + PURPLE = ?

25. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Your task is to make 8 when adding together either 2 or 3 unique digits from 1-9. There are just FIVE possible ways of doing this, can you list them?

26. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the target answer of 18 by using each of the four numbers 2, 6, 7, 10 exactly once each and having + – x ÷ available.

27. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem After analysing the first three sets of numbers, find the value of ? in the fourth set: 6-2-9 = 3 / 7-1-3 = 4 / 4-2-7 = 1 / 4-3-6 = ?

28. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Tyson, Usain and Johan were friends who were taking part in a race. They finished first, second and third and wore yellow, red and blue, but can you work out which position they each came and the colour shirt they wore from these two clues: Johan did not win and wasn’t wearing blue Tyson wore red and overtook the person who was in second place just before the line

29. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must visit every square below, just once each, starting at 1 and finishing at 49 by inserting the missing numbers from 1- 49. When moving from number to number, you can move just one square at a time in any direction, including diagonally. x13 x x x x 5 x x18 x x x x 16 48 x x20 9 x 45 x49 x x 1 2 x43 x x x23 x 37 x39 3331 x x x35 x x29 27 x

30. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem We had a palindromic date earlier this year in the UK, namely 21 February 2012, written as 21.02.2012. When is the next one due, if the date is represented in the exact same format of 8 digits (dd.mm.yyyy)?

31. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 12 letters shown below with 0, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9 so all three lines work out perfectly: A + B = 1 = C - D E + F = 12 = G x H I + J = 3 = K ÷ L

32. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the answer of 42 by using the formula (a x b) ± c, where a b c are three unique digits from 0-9. One way of making 42 is (9 x 4) + 6, so can you find the other THREE?

33. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Your task is to achieve 32 when receiving your card of three numbers. You must use each number once, with + – x ÷ available. An example of two cards that would allow you to get 32 are: Card 1 – 2 5 6 as (5 x 6) + 2 = 32 Card 2 – 4 4 4 as (4 + 4) x 4 = 32 List THREE other cards which would enable you to arrive at 32. Remember, the range of numbers on each card are 1-6.

34. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 12 letters shown below with 0, 1, 1, 2, 2, 3, 4, 5, 5, 8, 9, 9, so all three lines work out: A + B = 3 = C - D E + F = 8 = G x H I + J = 1 = K ÷ L

35. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem From each of the three groups of numbers below, you must arrive at the target answer of 25 by using the four digits exactly once each, and with + – x ÷ available: 3, 3, 4, 4 5, 7, 7, 9 2, 6, 7, 8

36. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem As there’s just 28 days to the start of the Olympic Games, you must arrive at the answer of 28 by using the formula (a x b) ± c, where a b c are three unique digits from 1-9. One way is (6 x 5) – 2 = 28, can you find the other FOUR ways?

37. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 12 letters shown below with 0, 1, 1, 2, 3, 4, 5, 5, 6, 7, 9, 9 so all three lines work out: A + B = 4 = C - D E + F = 18 = G x H I + J = 7 = K ÷ L

38. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ when you see ? so the result of each of the three 4-number calculations will equal 18 when you work one step at a time from Left to Right (no brackets): 8 ? 4 ? 7 ? 4 = 18 4 ? 6 ? 4 ? 3 = 18 5 ? 2 ? 8 ? 2 = 18

39. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Try and arrive at the target answer of 24 by using each of the numbers 1, 4, 6, 9 exactly once each, with + – x ÷ available. Extension Problem As above, make 24 by using each of the numbers 1 3 6 9 exactly once each.

40. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using the numbers 4, 8, 12 once each, with + – x ÷ available, which numbers from 1-30 are mathematically possible to achieve?

41. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem In the 2008 Beijing Olympics, the host country, China, and the United States were the top two countries in the official Medals Table, as shown below: China – 51 Gold; 21 Silver; 28 Bronze USA – 36 Gold; 38 Silver; 36 Bronze In our own 7puzzle Olympic Medals Table, we awarded 3 points for every Gold, 2 points for a Silver and 1 point for a Bronze. Using our scoring system, which country would top the table and by how many points?

42. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem 1896 was the year of the first modern Olympic Games in Athens. Since then, the Olympics have been held every four years, except 1916 1940 and 1944 when they were cancelled due to World Wars I and II. How many have therefore taken place prior to the Games of the XXXth Olympiad in London?

43. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Your task is to make a list of 2-digit numbers, in ascending order, which does not contain any multiples of 4, 5 or 6, nor any prime numbers, square numbers or cube numbers. What is the 7th number in your list?

44. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem At a child’s birthday party, there are four mothers each with one child. The four children are aged 1, 2, 3 and 4. Read these seven facts: It is Prue’s child’s birthday party Millie is not the oldest child Sue had Lily 18 months ago Lou’s child will be 3 next birthday Billy is older than Tilly Koo’s child is the oldest Tilly is older than Lou’s child Who’s child is whose, and how old is each child?

45. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem At a child’s birthday party, there are four mothers each with one child. The four children are aged 1, 2, 3 and 4. Read these seven facts: It is Prue’s child’s birthday party Millie is not the oldest child Sue had Lily 18 months ago Lou’s child will be 3 next birthday Billy is older than Tilly Koo’s child is the oldest Tilly is older than Lou’s child Who’s child is whose, and how old is each child?

46. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Time is dragging by at work for Jimmy. At noon, he looks over at the clock on the wall. The big hand is on the seven while the little hand is between the four and the five. What time is it?

47. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem There were 30 groups of golfers taking part in the final day of a tournament and an 11-minute gap between each group’s official starting time from the 1st tee. If the first group teed off at 9.30am, what time did the last group tee off?

48. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Try and arrive at the target answer of 7 by using each of the numbers 7, 7, 7, 7 exactly once each, with + – x ÷ available.

49. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Add together: the 7th Prime number the 7th Square number the 7th 2-digit number the 7th whole number that contains a ’7′ What is your answer?

50. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Try and arrive at the target answer of 24 by using each of the numbers 5, 7, 8, 8 exactly once each, with + – x ÷ available.

51. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Find the first seven EVEN numbers that are not multiples of 3, 5 or 7. What is the 7th number in your list?

52. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Starting from 1, add together the first SEVEN ODD numbers that do not contain a 3, 5 or 7 as part of their number, or are not divisible by 3, 5 or 7. What is your answer?

53. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem What is the sum of the 1st 100 whole numbers, that is 1 + 2 + 3 + 4 +... + 99 + 100?

54. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Find the first SEVEN whole numbers, above 20, that do not contain a 3, 5 or 7 as part of their number, or are not multiples of 3, 5 or 7. What is the 7th number in your list?

55. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the answer of 10 by using the formula (a x b) ± c, where a, b, c are three unique digits from 2-9. If (4 x 3) – 2 = 10, list the other FIVE ways of making 10, keeping to the above rules.

56. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 12 letters shown below with 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8 so all three lines work out: A + B = 5 = C - D E + F = 9 = G x H I + J = 8 = K ÷ L

57. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of each of these 5-number calculations, when working one step at a time from Left to Right (with no brackets), is 23 in each case: 3 ? 3 ? 3 ? 3 ? 1 = 23 4 ? 4 ? 4 ? 4 ? 3 = 23 5 ? 5 ? 5 ? 5 ? 2 = 23

58. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem After looking at the first three sets of numbers, find the value of ? in the fourth set: 6-2-2 = 8 / 7-3-5 = 6 / 7-2-4 = 6 / 6-3-5 = ?

59. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem As there’s just 39 days to the start of the Olympic Games, you must arrive at the answer of 39 by using the formula (a x b) ± c, where a, b, c are three unique digits from 1-9. One way of getting there is (6 x 5) + 9; can you find the other SEVEN ways?

60. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You notice, when stopping at a petrol station, that the reading on your car’s dashboard is a palindrome as it has travelled 15951 miles in total. How many more miles must you drive until the reading becomes another palindromic number?

61. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem On a normal dartboard, you need to score 69 to win the game, but have just TWO darts left. Apart from TREBLE 11 DOUBLE 18, show the other FIVE ways can you do this when ending a typical darts match in the proper manner.

62. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 12 letters shown below with 0, 1, 1, 2, 2, 3, 3, 4, 6, 6, 7, 7 so all three lines work out: A + B = 2 = C - D E + F = 9 = G x H I + J = 7 = K ÷ L

63. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Your task is to arrive at the target answer of 24 by using each of the numbers 2, 3, 7, 9 exactly once each and having + – x ÷ available.

64. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Your task is to arrive at the target answer of 24 by using each of the four numbers 0.5, 1, 5, 10 exactly once each and having + – x ÷ available.

65. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the answer of 37 by using the formula (a x b) ± c, where a b c are three unique digits from 1-9. One way of achieving this is (7 x 5) + 2, you must find the other SEVEN ways.

66. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Starting from 1, find the total of the first SEVEN whole numbers that do not contain a 3, 5 or 7 as part of their number, or are not multiples of 3, 5 or 7.

67. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Imagine to win the game, you had to achieve 30 when receiving your card. You must use each number once, with + – x ÷ available. An example of two cards that would allow you to make 30 are: Card 1 – 1 5 6 as (5 x 6) x 1 = 30 Card 2 – 4 6 6 as (6 x 4) + 6 = 30 Can you list at least FIVE other cards that would enable you to arrive at 30 and win the game?

68. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the letters A B C D and E with the digits 1 2 3 4 and 5 so that the following equation works: AB x C = DE

69. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using ALL six numbers 8, 12, 19, 19, 20, 48 once each, and with + – x ÷ available, today’s task is to arrive at the target answer of 432.

70. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 6- number calculation is 39 when working one step at a time from Left to Right (with no brackets): 3 ? 9 ? 3 ? 9 ? 3 ? 9 = 39

71. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using ALL six numbers 8, 12, 19, 19, 20, 48 once each, and with + – x ÷ available, try and arrive at the target answer of 408.

72. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem List SEVEN numbers that total 101, but: each number must be at least 4 away from one another the list must contain THREE square numbers

73. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 12- number calculation is 36. You must work one step at a time from Left to Right (and no brackets allowed) and all four operations have to be used: 1 ? 3 ? 5 ? 7 ? 9 ? 2 ? 4 ? 6 ? 8 ? 8 ? 3 ? 6 = 36

74. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You have a 6-sector dartboard containing the numbers 16, 17, 23, 24, 39, 40. Using some darts, your task is to achieve a score of EXACTLY 100 when adding your scores together. You can throw as many darts as you want and they can land in each sector more than once. There is only ONE way of achieving 100. How can it be done?

75. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the answer of 23 by using the formula (a x b) ± c, where a b c are three unique digits from 1-9. If (7 x 2) + 9 is one such way of making 23, how many different ways are there in all?

76. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 7- number calculation is 35. You must work one step at a time from Left to Right (and no brackets allowed): 6 ? 2 ? 7 ? 9 ? 5 ? 3 ? 8 = 35

77. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? below, so the result of the 7-number calculation is 30. You must work one step at a time from Left to Right (and no brackets allowed). To really test the puzzle enthusiasts, all four arithmetical operations must be used at some point in the calculation below: 4 ? 1 ? 7 ? 6 ? 2 ? 2 ? 1 = 30

78. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – or x each time you see ? so the result of this 7- number calculation is 25. You must work one step at a time from Left to Right (and no brackets allowed): 1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 = 25

79. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 7- number calculation is 15. You must work one step at a time from Left to Right (with no brackets) and all four arithmetical operations shown above must be used at some point: 7 ? 2 ? 5 ? 1 ? 4 ? 6 ? 3 = 15

80. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Try and arrive at the target answer of 24 by using each of the numbers 2, 4, 4, 5 exactly once each, with + – x ÷ available

81. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the target answer of 32 by using 2, 8, 8, 9 exactly once each and having + – x ÷ available.

82. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem After analysing the first three sets of numbers, find the values of x and y in the fourth and fifth sets: 7-2-3 = 13 / 6-3-7 = 8 / 3-5-5 = 6 / 5-1-7 = x / 8-y-10 = 15

83. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You must arrive at the target answer of 24 by using 1.5 2 2.5 4.5 exactly once each and having + – x ÷ available to you.

84. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Try and arrive at the target answer of 24 by using each of the numbers 1, 3, 8, 8 exactly once each, with + – x ÷ available.

85. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using the numbers 4, 5, 6 once each, with + – x ÷ available, which target numbers from 1-30 is it mathematically possible to achieve?

86. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the end result of this 7- number calculation is 10. You must work one step at a time from Left to Right (with no brackets), and all four arithmetical operations shown above must be used at some point in your answer: 1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 = 10

87. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 16 letters below with digits from 0-9. Can you make all four lines work out if the digits inserted can only be used a maximum of TWICE each? A + B = 12 = C + D E + F = 1 = G – H I + J = 9 = K x L M + N = 2 = P ÷ R

88. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Your task is to arrive at the target answer of 24 by using each of the numbers 2, 2, 6, 9 exactly once each and having + – x ÷ available. Can you do it?

89. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem The rule for a sequence of numbers is: if EVEN, halve it if ODD, subtract 1 So, if starting at 50, the sequence would be 50, 25, 24, 12, 6, 3, 2, 1, thus taking 7 steps to get from 50 down to 1. Following the above rules, which starting number between 50 and 100 would give you the most amount of steps when eventually arriving at 1?

90. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 7- number calculation is 31. You must work one step at a time from Left to Right (and no brackets allowed): 7 ? 3 ? 9 ? 6 ? 5 ? 3 ? 6 = 31

91. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 7- number calculation is 22 when working one step at a time, from Left to Right (with no brackets), and using ALL four operations in your calculation: 1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 = 22

92. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 7- number calculation is 37 when working one step at a time from Left to Right (with no brackets): 2 ? 9 ? 6 ? 3 ? 2 ? 4 ? 5 = 37 You MUST use all four arithmetical operations in your answer!

93. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Insert + – x or ÷ each time you see ? so the result of this 7- number calculation is 41 when working one step at a time from Left to Right (with no brackets). To add a little extra spice to this particular question, ALL four arithmetical operations must be used: 8 ? 4 ? 5 ? 6 ? 9 ? 8 ? 7 = 41

94. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem You are taking part in the Olympic 800 metres Final. As the race nears the halfway point, you suddenly accelerate and overtake the runner who was in 2nd place. What position are you in now?

95. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem A boat floats in the harbour at low tide. A ladder is fixed to the side of the boat, and seven rungs of the ladder are showing above the waterline. If the rungs are 25cm apart and the sea level rises at a rate of 40cm per hour, how many rungs will be showing above water after three hours?

96. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using ALL six numbers 19, 08, 19, 48, 20, 12 once each, and with + – x ÷ available, your task is to arrive at the target answer of 456.

97. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem When replacing the 16 letters below with digits from 0-9, each digit can only be used a maximum of TWICE. Can you make all four lines work out perfectly? A + B = 16 = C + D E + F = 6 = G – H I + J = 10 = K x L M + N = 9 = P ÷ R

98. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 16 letters shown below with 0, 0, 1, 1, 2, 2, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9 so that the four lines work out: A + B = 15 = C + D E + F = 2 = G – H I + J = 8 = K x L M + N = 1 = P ÷ R

99. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Using ALL six numbers 8, 12, 19, 19, 20, 48 once each, and with + – x ÷ available, can you arrive at the target answer of 480?

100. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 16 letters shown below with 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8 so that the four lines work out: A + B = 12 = C + D E + F = 5 = G – H I + J = 10 = K x L M + N = 2 = P ÷ R

101. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Replace the 16 letters shown below with 0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9 so that the four lines work out: A + B = 9 = C + D E + F = 7 = G – H I + J = 12 = K x L M + N = 6 = P ÷ R

102. F IND MORE PUZZLES AT HTTP ://7 PUZZLEBLOG. COM / HTTP ://7 PUZZLEBLOG. COM / Random Puzzle The Problem Imagine receiving three different cards which each contain three numbers as shown below: Card 1 – 2 6 10 Card 2 – 3 7 10 Card 3 – 4 8 10 For each card, use the numbers once each. With + – x ÷ available, find which target answers from 1-30 are common to ALL three cards.