Cayuga Heights 5th Grade Math Club
Solutions for February 26, 2016
Cryptarithms
Cryptarithms are puzzles where letters stand for different digits in an arithmetic problem. The problem
is usually to figure out which letters stand for which digits.
Often it helps to write equations using the letters. Algebra can then be used to solve for the letters.
Sometimes you can narrow the possibilities for a given letter down to a small number of choices, and
you just have to try them and see if there is a way to get a solution.
1. In this addition problem, different letters stand for different digits. What digit does Astand for?
4A
+A4
B C B
2. HA and AH represent two-digits numbers. If H A −AH = 18, what is the value of the expression
H−A?
Answer:
9
3. In this multiplication problem, different letters stand for different digits. What digit does Hstand for?
A H A
×A
T A D A
4. When the six-digit number 3456X7is divided by 8, the remainder is 5. Give both possible values of
the digit X.
Answer:
3 or 7. Notice 345600 is divisible by 8.
5. In this multiplication problem, A and B represent different digits. What is the 4-digit product?
A B
×B A
8
Answer:
42 ×24 = 1008
6. If 23AB3is divisible by 99, what is the two-digit number AB?
Answer:
46
7. The digits 1,2,3,4 and 5 are each used once to write a five-digit number ABCDE. The 3-digit number
ABC is divisible by 4, BCD is divisible by 5, and C DE is divisible by 3. Find the five-digit number
ABC DE.
Answer:
12,453 . Note Dmust be 5, so C+Emust have a remainder of 1 when divided by 3. So one of (C, E)must be
3 and the other is either 1 or 4. Since AB C is divisible by 4, Cmust be even—it must be 4. Then Eis 3. Then
Bmust be 2 since 14 is not divisible by 4, and Ais 1 by elimination.
