This document contains a series of math games and puzzles involving numbers. It begins with examples of mind-reading number games that involve picking a number and performing a series of steps to reveal personal details. Subsequent pages provide more elaborate versions of these games as well as number puzzles involving arranging digits or symbols to form different numbers. Activities are suggested for readers to play the games themselves and to generate their own variations. The document aims to make math learning fun through engaging puzzles and games.

1. Number Games
A Lesson in the “Math + Fun!” Series
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Apr. 2005 Number Games Slide 1

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 2003-04 and 2004-05 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 Revised
First Apr. 2005
Apr. 2005 Number Games Slide 2

3. What Number Did You Choose?
1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 10
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.
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 Slide 3

4. How Did the Game Work?
1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 10
2. Multiply the number by 9. 9 18 27 36 45 54 63 72 81 90
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 2. 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, . . .
Kangaroo
6. Use the last letter in your country’s name as the first letter of an animal.
Orange
7. Use the last letter of your animal’s name as the first letter of a color.
Apr. 2005 Number Games Slide 4

5. More Mind-Reading Games
1. Think of a 2-digit number (10-99).
2. Multiply your number by 5.
3. Add 500 to the result of step 2.
4. Add the number of your siblings.
5. 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.
1. Think of a number between 1 and 30.
2. Tell me in which of the five lists below the number appears.
List A: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
List B: 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30
List C: 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30
List D: 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30
List E: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A
C
E
Apr. 2005 Number Games Slide 5
B
D
E

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)
1. Think of a number between 1 and 20.
2. Tell me in which of the five lists below the number appears.
List A: 1 4 6 8 9 11 14 16 19
List B: 2 6 7 8 12 17 20
List C: 3 4 6 9 13 14 18 19 20
List D: 5 7 8 9 15 16 17 18 19 20
List E: 10 11 12 13 14 15 16 17 18 19 20
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 Slide 6

7. Activity 2: More Mind-Reading Games
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.
The Birthday Number Game
Your final result shows the
month and day of your birth
1. Pick any number and write it down
2. Add 10 to your number
3. Add 20 to the result
4. Subtract 4 from the result
5. Add 15 to the result
6. Subtract 5 from the result
7. Subtract your original number
1. Write down your BD month (1-12)
2. Multiply your number by 5
3. Add 6 to the result
4. Multiply the result by 4
5. Add 9 to the result
6. Multiply the result by 5
7. Add the day of your BD (1-31)
8. Subtract 165 from your result
Explain how this game works.
Apr. 2005 Number Games Slide 7

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
Referee
24 6
Player
1 18
12
Player 1
loses
Player
2
80 15
65 50
35
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 Slide 8

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
Start Player 1
531
231
Player 2
221
Player 1
Player 2
210
220 Player 1
010
Player 2
Loses!
000
Challenge:
1. Discover a winning strategy with (5, 3, 1), if you are the first player
2. Play the game with other numbers such as (7, 4, 2), (6, 5, 3), . . .
Apr. 2005 Number Games Slide 9

10. The Four 4s Puzzle
Use four 4s and any number of math symbols (such as +, -,
´, /, Ö, . . .) to form as many different numbers as possible.
0 = 4 – 4 + 4 – 4 Examples
1 = 4 – 4 + 4 / 4
2 = 4 / 4 + 4 / 4 or 4 – (4 + 4) / 4
3 = (4 + 4 + 4) / 4
4 = (4 + 4) / 4 + Ö4
5 = (4 ´ 4 + 4) / 4
6 = (4 + 4 + 4) / Ö4
8 = 4 ´ (4 / 4) + 4
7 = 4 + 4 – 4 / 4 or 44 / 4 – 4
9 = 44 / 4 – Ö4 or 4 / 4 + 4 ´ Ö4
10 = (4 + 4 / 4) ´ Ö4
11 = 44 / (Ö4 + Ö4)
12 = 4 ´ (4 – 4 / 4)
13 = 44 / 4 + Ö4
14 = 4 ´ (Ö4 + Ö4) – Ö4
15 = 44 / 4 + 4
16 = 4 ´ 4 + 4 – 4 or 4 ´ 4 ´ 4 / 4
17 = 4 ´ 4 + 4 / 4
18 = 4 ´ (Ö4 + Ö4) + Ö4
20 = 4 ´ (4 + 4 / 4)
22 = 4 ´ 4 + 4 + Ö4
19 = ë4.4 ´ 4.4û
21 = ë4.4 ´ 4 + 4û
23 = ë4 ´ (4 + Ö4) – .4û
24 = 4 ´ (Ö4 + Ö4 + Ö4)
25 = (4 + 4 / 4)Ö4
Apr. 2005 Number Games Slide 10

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

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.
Examples for 1993
0 = 1 ´ (9 – 9) ´ 3
1 = 1 + (9 – 9) ´ 3
2 = –1 + 9 – 9 + 3
3 = (1 + 9 – 9) ´ 3
4 =
5 =
6 = (1+ 9 / 9) ´ 3
8 =
7 =
9 =
10 =
Examples for 1994
0 = 1 ´ (9 – 9) ´ 4
1 = 1 + (9 – 9) ´ 4
2 = –1 – 9 / 9 + 4
3 = –1 + 9 – 9 + 4
4 = 1 ´ 9 – 9 + 4
5 = 1 + 9 – 9 + 4
6 = 1 + 9 / 9 + 4
8 = (1 + 9 / 9) ´ 4
10 = 1 ´ 9 – Ö9 + 4
7 = 1 ´ (9 / Ö9) + 4
9 = 1 + 9 + Ö9 – 4
Examples for 1995
0 = 1 ´ (9 – 9) ´ 5
1 = 1 + (9 – 9) ´ 5
2 =
3 =
4 =
5 = 1 – 9 / 9 + 5
6 =
7 =
8 =
9 =
10 = (1 + 9 / 9) ´ 5
Apr. 2005 Number Games Slide 12

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

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 Slide 14

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

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

17. By,
Viashnavi, VIII
Apr. 2005 Number Games Slide 17