1. A Lesson in the “Math + Fun!” Series
Number Games
A Lesson in the “Math + Fun!” Series
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Math has many uses in geography. This lesson focuses on the relationship of math to making and using maps.
Apr. 2005
Number Games

2. About This Presentation
This presentation is part of the “Math + Fun!” series devised by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during the and school years. The slides can be used freely in teaching and in other educational settings. Unauthorized uses are strictly prohibited. © Behrooz Parhami
Edition
Released
Revised
First
Apr. 2005
Apr. 2005
Number Games

3. What Number Did You Choose?
1. Pick a number from this list:
2. Multiply the number by 9. If the result has two digits, add the two digits;
otherwise leave the number alone.
3. Subtract 5 from the number that you got in step 2.
4. Pick the letter that corresponds to the number you got in step 3.
1 = A, 2 = B, 3 = C, 4 = D, 5 = E, 6 = F, 7 = G, 8 = H, etc.
5. Pick a country in Europe whose name begins with your letter.
A = Austria, . . .
B = Belgium, . . .
C = Croatia, . . .
D = Denmark, . . .
E = England, . . .
F = France, . . .
etc.
Orange kangaroo from Denmark
6. Use the last letter in your country’s name as the first letter of an animal.
7. Use the last letter of your animal’s name as the first letter of a color.
Apr. 2005
Number Games

4. How Did the Game Work?
1. Pick a number from this list:
2. Multiply the number by
If the result has two digits, add the two digits You get 9 in all cases!
3. Subtract 5 from the number that you got in step You get 4
4. Pick the letter that corresponds to the number you got in step 3.
1 = A, 2 = B, 3 = C, 4 = D, 5 = E, 6 = F, 7 = G, 8 = H, etc.
5. Pick a country in Europe whose name begins with your letter.
A = Austria, . . .
B = Belgium, . . .
C = Croatia, . . .
D = Denmark, . . .
E = England, . . .
F = France, . . .
Orange kangaroo from Denmark
6. Use the last letter in your country’s name as the first letter of an animal.
Kangaroo
7. Use the last letter of your animal’s name as the first letter of a color.
Orange
Apr. 2005
Number Games

5. More Mind-Reading Games
Think of a 2-digit number (10-99).
Multiply your number by 5.
Add 500 to the result of step 2.
Add the number of your siblings.
Double the result of step 4.
You got a 4-digit number that starts with 1, has your original 2-digit number in the middle, and double the number of your siblings at the end.
Think of a number between 1 and 30.
Tell me in which of the five lists below the number appears.
List A:
List B:
List C:
List D:
List E: A C E B D E
Apr. 2005
Number Games

6. Activity 1: Mind-Reading Game
Play the following mind-reading game with your friends and family
(First, discover how to tell the number if you know which lists it is in)
Think of a number between 1 and 20.
Tell me in which of the five lists below the number appears.
List A:
List B:
List C:
List D:
List E:
Challenge: Add a List F to the five lists given above, and complete the lists, so that you can play the game with numbers up to 40.
Apr. 2005
Number Games

7. Activity 2: More Mind-Reading Games
Pick any number and write it down
Add 10 to your number
Add 20 to the result
Subtract 4 from the result
Add 15 to the result
Subtract 5 from the result
Subtract your original number
I know what your number is!
Your final result is 36, isn’t it?
Explain how this game works.
Change the numbers to make your own game.
Write down your BD month (1-12)
Multiply your number by 5
Add 6 to the result
Multiply the result by 4
Add 9 to the result
Multiply the result by 5
Add the day of your BD (1-31)
8. Subtract 165 from your result
The Birthday Number Game
Your final result shows the month and day of your birth
Explain how this game works.
Apr. 2005
Number Games

8. Euclid’s Game for Two Players
A referee writes two numbers on the board
The two players take turns writing the difference of two numbers
already on the board, provided the difference is a new number
The player who cannot write a new number loses
Player 1
loses 24 6
Referee 80 15 35 65 50 18
Player 1 12
Player 2
The total number of values written on the board is
n = the larger number / greatest common divisor of the two numbers
If n is odd, player 1 wins
Apr. 2005
Number Games

9. Activity 3: The Game of Nim
Write three numbers on three lines
The two players take turns reducing one of the numbers
The player who makes the last move loses 5 3 1
Start
Player 1 2 3 1
Player 2 2 1
Player 1 2
Player 2 2 1
Player 1 1
Player 2
Loses!
Challenge:
Discover a winning strategy with (5, 3, 1), if you are the first player
Play the game with other numbers such as (7, 4, 2), (6, 5, 3),
Apr. 2005
Number Games

10. The Four 4s Puzzle
Use four 4s and any number of math symbols (such as +, -, , /, , . . .) to form as many different numbers as possible.
1 = 4 – / 4
0 = 4 – – 4
Examples
13 = 44 / 4 + 4
14 = 4  (4 + 4) – 4
2 = 4 / / 4 or 4 – (4 + 4) / 4
15 = 44 / 4 + 4
3 = ( ) / 4
16 = 4  – 4 or 4  4  4 / 4
4 = (4 + 4) / 4 + 4
17 = 4  / 4
5 = (4  4 + 4) / 4
18 = 4  (4 + 4) + 4
6 = ( ) / 4
19 = 4.4  4.4
21 = 4.4  4 + 4
23 = 4  (4 + 4) – .4
7 = – 4 / 4 or / 4 – 4
20 = 4  (4 + 4 / 4)
8 = 4  (4 / 4) + 4
9 = 44 / 4 – 4 or 4 /  4
22 = 4  4
10 = (4 + 4 / 4)  4
11 = 44 / (4 + 4)
24 = 4  (4 + 4 + 4)
12 = 4  (4 – 4 / 4)
25 = (4 + 4 / 4)4
Apr. 2005
Number Games

11. Activity 4: The Five 5s Puzzle
Use five 5s and any number of math symbols (such as +, -, , /, , . . .) to form as many different numbers as possible.
0 = 5  (5 / 5 – 5 / 5)
13 =
Examples
1 = 55 / 5 – 5 – 5
14 =
2 =
15 =
3 =
16 =
4 =
17 =
5 =
18 =
6 =
19 =
7 =
20 =
8 =
21 =
9 =
22 =
10 =
23 =
11 =
24 =
12 =
25 =
Apr. 2005
Number Games

12. Activity 5: Birth Year Puzzle
Use the digits in your year of birth, in order, plus any number of math symbols (+, –, . . .) to form the numbers from 0 to 10.
3 = (1 + 9 – 9)  3
4 =
5 =
2 = –1 + 9 – 9 + 3
6 = (1+ 9 / 9)  3
8 =
7 =
9 =
10 =
1 = 1 + (9 – 9)  3
Examples for 1993
0 = 1  (9 – 9)  3
3 = –1 + 9 – 9 + 4
4 = 1  9 – 9 + 4
5 = – 9 + 4
6 = / 9 + 4
8 = (1 + 9 / 9)  4
10 = 1  9 – 9 + 4
1 = 1 + (9 – 9)  4
Examples for 1994
2 = –1 – 9 / 9 + 4
7 = 1  (9 / 9) + 4
9 = 9 – 4
0 = 1  (9 – 9)  4
1 = 1 + (9 – 9)  5
2 =
3 =
4 =
5 = 1 – 9 / 9 + 5
6 =
7 =
8 =
9 =
10 = (1 + 9 / 9)  5
Examples for 1995
0 = 1  (9 – 9)  5
This puzzle becomes more or less difficult, depending on your birth year. It is pretty simple for most years. However, for someone born in 2005, it is hard: 0 = 2x0 + 0x5, 1 = 2^0 + 0x5 = 2.0x0.5, 2 = x5, 3 = , 4 = -2^ , 5 = 2x , 6 = 2^ , 7 = ; I got stuck a this point!
Apr. 2005
Number Games

13. Activity 6: Your Phone Number
Write down your phone number, with space between digits
Example:
Now, try to make as many different numbers as you can by
Putting + , - , , / signs between the digits.
0 =
1 =  3
2 =   3
3 =
4 =
5 =
6 =
7 =
8 =
Apr. 2005
Number Games

14. Another Game for Two Players
Put some playing cards (or numbers) in a row
Players take turns removing a card from either end of the row
At the end, add up the numbers to see who wins
Apr. 2005
Number Games

15. Game Tree 1 1 2 Player 1 Player 2 Player 1 Player 2 Player 1
Score for
Player 1
Player 2
Cards left
0 [ ] 0
6 [ ] 0
1 [ ] 0
Player 1
Player 2
1 [ ] 6
1 [ ] 2
6 [ ] 8
6 [ ] 1
Player 1
6 [4 8 6] 2
7 [5 4 8] 2
3 [5 4 8] 6
9 [2 5 4] 6
Player 2
6 [8 6] 6
6 [4 8] 8
7 [4 8] 7
7 [5 4] 10
3 [4 8] 11
3 [5 4] 14
9 [5 4] 8
9 [2 5] 10
Player who wins 1 1 2
Player 1
Apr. 2005
Number Games

16. Some Surprising Predictions
Answer these questions quickly.
If you pause, it won’t work.
What is 2 + 2?
What is 4 + 4?
What is 1 + 1?
What is 9 + 9?
What is 8 + 8?
What is 2 + 2?
What is the first vegetable that comes to your mind?
What is ?
What is 3 + 3?
Quickly, pick a number between 12 and 5
What is 4 + 4?
What is 5 + 5?
What is 6 + 6?
No one knows why these guesses work for most people.
What is 7 + 7?
What is 8 + 8?
Apr. 2005
Number Games

17. Next Lesson Special Numbers Thursday, May 19, 2005
The only number with letters
appearing in alphabetical order
What is special about 40? (Hint: Forty)
The smallest
perfect number
What is special about 6? (Hint: Divisible by 1, 2, 3)
The last Roman numeral
in alphabetical order
What is special about 38? (Hint: XXXVIII)
Apr. 2005
Number Games