Arithmetic Puzzles

Created by Inna Shapiro ©2008

Problem 1

Please, replace the “#” and “&” symbols with digits

# #

+ # &

1 9 7

Answer

9 9

+ 9 8

1 9 7

Problem 2

Please, replace the “#” and “&” symbols with digits

1 # # #

- & & &

1

Answer

1 0 0 0

- 9 9 9

1

Problem 3

Please, replace each letter with a digit:

aa + bcb = deed,

Note that each of those numbers is its own mirror image (left to right is same as right to left).

Answer

We must find digits, so that the sum looks like

aa + bcb = deed.

Obviously d=1 and b=9 =>

aa + 9c9 = 1ee1, that means that a=2,

22 + 9c9 = 1ee1 => e=0 and c=7

22 + 979 = 1001

Problem 4

Please, replace letters with digits

B D C E+ B D A E

A E C B E

Answer

5 2 4 0 + 5 2 1 0

1 0 4 5 0

Problem 5

Please, replace letters with digits

a 5 2 b- b 2 5 a

8 c d c

Answer

9 5 2 1- 1 2 5 9

8 2 6 2

Problem 6

How can you replace “#” and “&”

symbols?

1. #### + 1 = 1&&&&

2. 1&&&&&& - 1 = ######

Answers

1. 9999 + 1 = 10000

2. 1000000 – 1 = 999999

Problem 7

Can you change letters ‘a’ and ‘b’ to digits?

b

a a a a

+ a a a a

a a a a

b a a a a

Answer

2

9 9 9 9

+ 9 9 9 9

9 9 9 9

2 9 9 9 9

Problem 8

Please, replace letters with digits to get the correct answer

7abcdef : 5 = abcdef7

Answer

714285 : 5 = 142857

Problem 9

Max wrote two-digit number. Then he inserted 0 between the two digits. The result is nine times greater than original number.

What was the original number?

Answer

The original number is 45, when

Max added 0 he got 405,

45 * 9 = 405

Problem 10

Please add arithmetic signs and parenthesis to get correct answers:

5 5 5 5 = 3

5 5 5 5 = 4

5 5 5 5 = 5

5 5 5 5 = 6

5 5 5 5 = 7

Answer

(5 + 5 + 5) : 5 = 3

(5 * 5 – 5) : 5 = 4

(5 – 5) * 5 + 5 = 5

(5 * 5 + 5) : 5 = 6

(5 + 5) : 5 + 5 = 7