## What Digit Does Each Letter Represent?

This is what you know:

1. Each letter represents a different digit from 1 to 9

2. The total of each row is 17.

3. (B × B) + B + F = A

4. C × F = EF (a 2-digit number, not their product)

A B C

D E F

What digit does each letter represent?

A = 7

B = 1

C = 9

D = 8

E = 4

F = 5

A + B + C = 17

D + E + F = 17

B^{2} + B + F = A

C × F = EF

To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.

2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.

C × F = EF

9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.

3 Comments on "What Digit Does Each Letter Represent?"swathi says

June 15, 2015 @ 13:19

ABC

719 = 17

DEF

845 = 17

Ciel Takuro Yuki says

July 8, 2015 @ 10:03

oh..okay then

Crustal says

January 1, 2018 @ 15:02

I don’t know algebra yet so don’t teach me it yet

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