Fun Arithmetic

Created by Inna Shapiro ©2008

Problem 1

Max has ten cards with the digits 0, 1, 2,…9. He can arrange these cards into different 10-digit numbers.

What is the greatest number that he can get?

Answer

The greatest number should start with the greatest digit 9. The second digit will be the greatest of the rest, i.e. 8, and so on.

The greatest number is 9876543210.

Problem 2

A teacher has four cards with numbers.

The sum of these numbers is equal to 8.

When the teacher shows these cards to Mary and asks to multiply the numbers, Mary also gets 8.

What numbers are on the cards? Some numbers could be equal.

Answer

The numbers are

1, 1, 2, and 4.

Problem 3

Ron has five cards with the digit 1.

How can he arrange them to compose the number 100 using the arithmetic operations +, -, *, and / ?

Answer

100=111-11

Problem 4

Monty has five cards with the digit 5.

How can he arrange his cards to get the number 100 using the arithmetic operations +, -, *, and / ?

Answers

100=5*5*5-5*5

100=(5+5+5+5)*5

Problem 5

There are nine cards with different digits 1,2,3,4,5,6,7,8,9.

Can you compose number 100 using all these cards in the same order and the arithmetic operations +, -, *, and / ?

Answers

100=1+2+3+4+5+6+7+8*9

100=1*23+4+5+67-8+9

Problem 6

Can you replace # by arithmetic operations so that the following expression will be equal to 100? You can use parentheses.

1#2#3#4#5

Answer

100=1*(2+3)*4*5

Problem 7

Jerry has four cards with the digit 2.

How can he arrange these cards to get 0, 1, 2, 3, 4, 5, 6, 8, 9, or 10? Jerry can use arithmetic operations +, -, *, and /.

Answer

22-22=0

22:22=1

2:2+2:2=2

(2+2+2):2=3

2*2+2-2=4

Answer /continued/

2*2+2:2=5

2*2*2-2=6

2 +2+2+2=8

22:2-2=9

2*2*2+2=10

Problem 8

Can you put in parentheses so that this expression will be equal to 23?

7*9+12:3-2

Answer

23=(7*9+12):3-2

Problem 9

Can you put parentheses in the same expression to make it equal to 75?

7*9+12:3-2

Answer

75=(7*9+12):(3-2)

Problem 10

Put numbers into this table so that the sum of any three adjacent cells equals 15.

6 4

Answer

The number in each cell must be the same as the number in any cell three slots away from it. Let’s fill the table step by step.

6 6 6 4 6 6

6 4 6 4 6 4 6 4 6

6 5 4 6 5 4 6 5 4 6 5 4 6