Mystery Number 2Logic puzzles require you to think. You will have to be logical in your reasoning.
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
A = 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.
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