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50 More Puzzles The answer for most puzzles is in the notes section of each slide. You will need to scroll down to find it. For a few puzzles, the answer is on the next slide (this is indicated). Pictures are included on most slides. Some will help, others will lead you astray!

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**The puzzles are in 3 sections: Logic / Lateral thinking Maths **

There is a points rating for each puzzle and each puzzle is numbered. The puzzles are in 3 sections: Logic / Lateral thinking Maths Maths Investigations

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**Logic / lateral thinking**

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1 point 1 James is in a balloon off the coast of Norfolk. He drops an empty plastic Coke bottle, an empty glass wine bottle and a full glass whisky bottle. Which will hit the ground first? None – they will all hit water.

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2 points 2 There are 10 pigeons in the large ash tree outside Farmer Giles’ house. He shoots 1/5 of them. How many are left on the tree? None because the rest fly off.

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3 points 3 A man lives on his own. One day, he switches off the light, leaves his house and ten people die. Explain. He lives in a lighthouse. As the light was switched off, a ship was wrecked on the rocks.

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**Which side of a cat has more fur?**

4 3 points Which side of a cat has more fur? The outside

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2 points 5 Jake is hiding under the dining room table. It is his sister’s party. He counts 12 legs. Ten minutes later, he is alone in the room yet he can still see 4 legs. Explain. He can see the 4 legs of the table.

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1 point 6 If you are running in a race and overtake the person who is in second place, what place will you be in? second

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**If you overtake the person in last place, what place will you be in?**

1 point 7 If you overtake the person in last place, what place will you be in? You can’t overtake the person in last place!

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**How many f’s are there in the following sentence?**

2 points 8 How many f’s are there in the following sentence? Finished files are the result of years of scientific study combined with the experience of years. 6

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**How many houses are there on my side of the road?**

2 points 9 My house is the 6th house from the north end of the road and the 5th house from the south end of the road. How many houses are there on my side of the road? 10

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3 points 10 Can you name 3 days in row without using the words: Tuesday, Thursday or Saturday? Yesterday, today tomorrow

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2 points 11 You have nine sticks. Without cutting any in half how can you make ten? Answer on next slide.

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**James drives his car at 40 mph from Sheffield to London. **

2 points 12 James drives his car at 40 mph from Sheffield to London. Driving the other way from London, Mary speeds at 80 mph towards Sheffield. It is 160 miles from Sheffield to London. Who will be further away from Sheffield when they meet? Nobody. They will both be the same distance from Sheffield.

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2 points 13 A man who is mute goes into a shop. He wants to buy a toothbrush. By miming the action of brushing his teeth, he lets the shopkeeper know what he needs. A blind person walks in next. She needs some toilet rolls. How does she communicate this to the shopkeeper? She asks for it using her voice.

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**The next puzzle needs to read but not shown.**

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2 points 14 There are seven tea cups sitting on a table. One falls off. How many are left? Answer 6 not 69 as it is 7 tea cups not 70 cups.

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3 points 15 John already has 9 points on his driving license. On Wednesday, he went the wrong way up a one way street, failed to see the red lights as he passed through before speeding off towards his home. He was seen by 3 policemen and a traffic warden yet was not stopped. Explain. He was on foot.

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3 points 16 A nurse gives you 7 pills to take. You have to take one every half hour. How long will it be before you have eaten them all? 3 hours. eg 1:00, 1:30, 2:00, 2:30, 3:00, 3:30, 4:00

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**What is the next letter in the sequence? F M A M J J A S**

3 points 17 What is the next letter in the sequence? F M A M J J A S O for October

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**What is the next letter in this sequence? O T T F F S S**

5 points 18 What is the next letter in this sequence? O T T F F S S E for eight

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6 points 19 You are on an island. It has steep cliffs preventing you from jumping into the sea. There is a fire on the west of the island and the wind is blowing it towards you. You have a box of matches in your pocket. What can you do to survive? Light a fire and then retreat west. As the wind blows the fire to the east, an area of burnt ground will be left which you can go into and which the larger fire will not be able to cross. Use your matches to start a smaller fire in the middle of the island. When the larger fire reaches the burnt out bit, it won’t be able to cross it.

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**Look at this snowy scene.**

20 Look at this snowy scene. Continued on next slide.

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**Look at the fluffy clouds in this picture.**

20 Look at the fluffy clouds in this picture. Continued on next slide.

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**Look at this plain paper.**

20 Look at this plain paper. Continued on next slide landscape portrait

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20 What do cows drink? water

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**invite How can you remove 4 letters from the word invite to leave 6?**

8 points 21 How can you remove 4 letters from the word invite to leave 6? invite Remove the first 2 and last 2 letters to leave vi (6 in Roman numerals)

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**What 4 letter word reads the same forwards, backwards and upside down?**

8 points 22 What 4 letter word reads the same forwards, backwards and upside down? Answer on next slide

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22 NOON

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10 points 23 There are 4 men on a sinking ship. A rickety bridge separates them from safety. The bridge will only take 2 people at a time. Alf would take one minute to cross the bridge, Bert 2 minutes, Cedric 5 minutes and Dominic 10 minutes. It is night and they have one torch. This has to be taken across the bridge and returned for anyone else crossing the bridge. It cannot be thrown. If 2 people cross a bridge, they travel at the speed of the slowest person. In 17 minutes the ship will sink and the bridge will collapse with it. How can they get to safety in this time? Answer on next slide.

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23 Who goes where Time taken Total time taken Alf & Bert cross 2 mins Alf returns with torch 1 min 3 mins Cedric & Dominic cross 10 mins 13 mins Bert returns with torch 15 mins Alf & Bert cross one last time 17 mins

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Maths puzzles

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2 points 24 Mary has 22 sweets. She gives her friends all but 10 of them. How many does she have left? 10

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3 points 25 Do this mental arithmetic: start with 1000, add 40. Then add another 1000 and 30. Add 1000 more followed by 20. Finally add 1000 followed by 10. What do you get? 4100

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3 points 26 I have some hamsters and some cages. If I put 1 hamster per cage, I have a hamster without a cage. If I put 2 hamsters per cage, I have an empty cage. How many hamsters and cages have I got? 4 hamsters and 3 cages

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4 points 27 Joe counted the number of peanuts he ate every day for a week. He worked out that he had eaten an average of 13 peanuts per day. How many peanuts must he eat on the 8th day to bring his average down to exactly 12? 5 7 x 13 =91 8 x 12 = 96 96 – 91 = 5

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4 points 28 Callum spreads his money out on the table. It is all in 5p pieces. Half of his money has heads facing up. He turns over 5 tails. Now ¾ of the money has heads facing up. How much money does he have? Jessica has her money in 10p pieces. ⅓ of it has heads facing up. She turns over one coin. ¼ now has heads facing up. How much money does she have? Carol has her money in 2p pieces. ½ is heads up. She turns 4 coins over and finds that ⅓ of her money now has heads facing up. How much money does she have? Callum 20 x 5p = £1 Jessica 12 x 10p = £1.20 Carol 24 x 2p = 48p

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5 points 29 Bert has some shells. If he sorts them into 2 equal piles, he has 1 left over. In fact if he sorts them into 3 piles, 4 piles or 6 piles, he still has 1 left over. When he sorts them into 5 piles, he has 4 left over. Finally he finds that he has none remaining when he sorts them into 7 equal piles. How many shells does he have? 49

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5 points 30 How can you put 15 sheep into 4 pens and have an odd number of sheep in each pen? Put 5 sheep each in 3 pens then put a large pen round the 3 smaller pens.

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5 points 31 A train is 1km in length. It is travelling at 60km/hr. It enters a tunnel which is 1km in length. How long will it take for the whole train to pass through the tunnel? 2 minutes

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**Boat 1 returns every 2 hours. Boat 2 returns every 3 hours. **

5 points 32 Four boats continuously leave the harbour to take passengers on fishing trips. Boat 1 returns every 2 hours. Boat 2 returns every 3 hours. Boat 3 returns every 4 hours. Boat 4 returns every 5 hours. If they all leave the harbour together, after how many hours will they first be all together in the harbour again? 60 hours

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**How many cards do they each have?**

6 points 33 Harry, Bert and Fred collect football cards. Together they have 450 cards. Harry has 110 more than Bert who has 50 more than Fred. How many cards do they each have? Fred 80 Bert 130 Harry 240

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**How many questions did Millie get right?**

6 points 34 Millie is due to do a Maths test. Her mother says she will give her 9p for every question she gets right but that Millie must pay her mum 5p for every wrong answer. There are 28 questions. After the test is marked, neither Millie nor her mother need to pay each other. How many questions did Millie get right? 18 correct (18 x 5 = 90 = 10 x 9) 10 incorrect

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**How many sweets did Becky and Samantha start with?**

6 points 35 Becky had 3 times as many sweets as Samantha. They each gave 14 sweets to Ellie. Now Becky had 7 times as many sweets as Samantha. How many sweets did Becky and Samantha start with? Becky 63 then 49 Samantha 21 then 7

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**In a field there are pink pigs and black pigs. **

6 points 36 In a field there are pink pigs and black pigs. A pink pig can see 5 times as many black pigs as pink pigs. A black pig can see twice as many black pigs as pink pigs. How many black pigs and pink pigs are in the field? 2 pink 5 black

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6 points 37 You are staring into a wood. You can see 22 eyes and 32 legs. These belong to foxes and owls. How many owls and how many foxes are there? 5 foxes & 6 owls (5 x x 2) = 32 legs

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9 points 38 You are in the wood with the foxes and owls. This time there are 24 eyes and 38 legs. How many foxes and owls are there? There are 7 foxes, 4 owls and you! (7 x x x 2) = 38 legs

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**Shannon takes all of her money out of her bank. **

7 points 39 Shannon takes all of her money out of her bank. She spends 75% of it on a new phone. She then spends 75% of the remaining money on books. Of the remaining money, she spends 75% on a game. She is left with £2 which she spends on sweets. How much money did she take out of her bank? Answer on next slide.

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**Shannon withdrew £128 from her bank.**

39 Shannon withdrew £128 from her bank. Total 75% Spent on Leaving 128 96 phone 32 24 books 8 6 game 2 sweets

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**He had 5 sons and 3 daughters. How much would each person receive?**

8 points 40 Albert Moneybags died leaving £108,000. His will stated that his widow should receive twice as much as each son and that each son should receive three times as much as each daughter. He had 5 sons and 3 daughters. How much would each person receive? Daughters: 3 x 4500 = 13,500 Sons: x 13,500 = 67,500 Widow: 1 x 27,000 = 27,000

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8 points 41 Three guests book rooms in a hotel for £30 in total. The manager realises they should have a discount of £5. He gives the receptionist £5 to return to the guests. She reckons they will have a hard job dividing up £5 between 3 people so she gives them £1 each and keeps the remaining £2 for herself. So out of the original £30, the guests have paid £27, the receptionist has £2. What has happened to the last £1? The 3 guests paid £27 after their refund. Of that the hotel received £25 and the receptionist £2. There is no missing £1.

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9 points How many eggsactly? 42 Fred has a basket of eggs. He sells half his eggs plus half an egg to Tom. He then sells half the remainder plus half an egg to Sarah. After that, he sells half the remainder plus half an egg to Courtney. Half the remainder plus half an egg was sold to Wilfred. Finally, Fred boils the one egg he is left with and eats it for lunch. How many eggs were in the basket to start with? Answer on the next slide.

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**There were 31 eggs in the basket to start with.**

42 There were 31 eggs in the basket to start with. Name Eggs sold to Eggs left 31 Tom 16 15 Sarah 8 7 Courtney 4 3 Wilfred 2 1 Fred

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9 points 43 4158=3 7953=1 8842=5 3467=2 1753=0 8888=8 6247=1 8046=6 6812=3 Can you explain this? It is a very simple principle. The number on the right shows the number of enclosed shapes in the number on the left. 8 has 2 enclosed shapes; 4, 6, 9 & 0 have 1 enclosed shape.

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**Fred wants to get into a club. He watches the entrance. **

10 points 44 Fred wants to get into a club. He watches the entrance. “Twelve,” says the doorman. “Six,” replies a fat man. He is admitted. “Six,” the doorman says to a tall woman. “Three,” she says and is also let in. Fred thinks he understands. “Four,” says the doorman. “Two,” replies Fred. He is not allowed in. What should he have said? 4. You reply with the number of letters in the number the doorman says.

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**Answer on the next slide.**

10 points 45 12 litres of beer have been delivered to the head teacher of Alehouse Primary School. He wants to give 11 litres to the staff to drink and keep 1 litre for himself. He only has the full 12 litre barrel, a 7 litre container and a 3 litre container. None of the containers have any scales on them. How can he measure out 11 litres and 1 litre by pouring the beer between the three containers? Answer on the next slide. Start 12 litre barrel 7 litre jug 3 litre jug 12 litres 7 litres 3 litres

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45 12 litre 7 litre 3 litre start 12 5 7 4 3 8 1 11

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Investigations

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**What other amounts can you make?**

6 points 46 Using 4 British coins (no more or no less) can you make each of the amounts from 4p to 37p inclusive? You can use more than 1 of the same coin. What other amounts can you make?

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46 4 = 5 = 6 = 7 = 8 = 9 = 10 = 11 = 12 = 13 = or 14 = or 15 = 16 = 17 = 18 = 19 = 20 = 21 = 22 = 23 = or 24 = or 25 = or 26 = or 27 = or 28 = 29 = 30 = 31 = 32 = 33 = 34 = 35 = 36 = 37 =

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**The number 15 has 2 digits. If you add them together, you get 6 **

5 points 47 The number 15 has 2 digits. If you add them together, you get 6 1 + 5 = 6 How many numbers can you find where the sum of the digits = 6? No zeros and no decimal points. 32 numbers to find (including 24). Answers on the next slide.

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47 111111 24 42 11112 11121 11211 12111 21111 411 141 114 33 2211 2121 2112 1221 1212 1122 51 15 3111 1311 1131 1113 222 312 321 123 132 213 231 6

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8 points 47 Further investigations. How many different numbers would you be able to make for these numbers using the same rules (no zeros and no decimal points)? 11 12 13 14 15 (already done) 16 Do you see a pattern? Answers on next slide.

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47 Number Combinations 11 2 12 4 13 8 14 16 15 32 64

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**Alfy serves one scoop of ice cream in one flavour – apple.**

8 points 48 Ice cream delight. Alfy serves one scoop of ice cream in one flavour – apple. There is only one type of cone you can buy from Alfy. Continued on next slide. A

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**How many different ice cream cones does Bertie sell?**

48 Bertie always serves 2 scoops stacked vertically. He has 2 flavours: apple and blueberry. How many different ice cream cones does Bertie sell? Continued on next slide. B A

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**How many different ice cream cones does Carol sell?**

48 Carol always serves 3 scoops stacked vertically. She has 3 flavours: apple, blueberry and cherry. How many different ice cream cones does Carol sell? Continued on next slide. C B A

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**How many different ice cream cones does Carol sell?**

48 Dawn always serves 4 scoops stacked vertically. She has 4 flavours: apple, blueberry, cherry and damson. How many different ice cream cones does Carol sell? Continued on next slide. D C B A

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48 Without drawing out the cones, can you work out how many Edward would sell, if he always served 5 scoops and stocked 5 different flavours – apple, blueberry, cherry, damson and elderberry. Answers on next slide.

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48 Name Scoops Combinations How it works Alfy 1 Bertie 2 1 x 2 Carol 3 6 1 x 2 x 3 Dawn 4 24 1 x 2 x 3 x 4 Edward 5 ? 1 x 2 x 3 x 4 x 5

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8 points 49 How many times would you see 3 of the same numbers in a row in 24 hours on an ordinary 4 digit 24 hour digital clock? 1 1 : 1 4 00:00 00:01 00:02 00:03 00:04 00:05 00:06 00:07 00:08 00:09 01:11 02:22 03:33 04:44 05:55 10:00 11:10 11:11 11:12 11:13 11:14 11:15 11:16 11:17 11:18 11:19 12:22 13:33 14:44 15:55 20:00 21:11 22:22 23:33

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8 points 50 How many times would you see 3 of the same numbers in a row in 12 hours on an ordinary 4 digit 12 hour digital clock? 1 1 : 1 4 01:11 02:22 03:33 04:44 05:55 10:00 11:10 11:11 11:12 11:13 11:14 11:15 11:16 11:17 11:18 11:19 12:22

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