### Brain Teasers

# Mystery Number 2

There is a ten-digit mystery number, represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1) A * F = CE

2) B * H = JI

3) D * G = BH

4) G * I = CF

1) A * F = CE

2) B * H = JI

3) D * G = BH

4) G * I = CF

### Answer

5738069241A = 5, B = 7, C = 3, D = 8, E = 0, F = 6, G = 9, H = 2, I = 4, J = 1

1) A * F = CE, 5 * 6 = 30

2) B * H = JI, 7 * 2 = 14

3) D * G = BH, 8 * 9 = 72

4) G * I = CF, 9 * 4 = 36

A) If a number has 5 as a units digit, then one of its factors must also have 5 as a units digit. Therefore, the following can not be 5: E, F, H, I.

B) If any multiplier is 0, then the product is also 0. Therefore, the following can not be 0: A, B, D, F, G, H, I.

C) If any multiplier is 1, then the product equals the other multiplier. Therefore, the following can not be 1: A, B, D, F, G, H, I.

D) Through trial and error, it can be found that C and J can not be 0. Therefore, E = 0.

E) To satisfy equation #1, A = 5 and F must be an even number and C must be 1 through 4.

F) Through trial and error, it can be found that C can not be 1. Therefore, J = 1.

G) Through trial and error, it can be found that C can not be 2 or 4. Therefore, C = 3, which results in F = 6, G = 9, and I = 4.

H) To satisfy equation #2, B and H must 2 and 7 or 7 and 2. This results in D = 8.

I) To satisfy equation #3, B = 7 and H = 2.

Hide Answer Show Answer

## What Next?

**Solve a Similar Brain Teaser...**

Or, get a random brain teaser.

If you become a registered user you can vote on this brain teaser, keep track of

which ones you have seen, and even make your own.

## Follow Braingle!