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## Mystery Number 4

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #44416 Fun: (2.11) Difficulty: (2.8) Category: Logic Submitted By: cnmne

There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

Note: a leading zero (0) can be used in the following equations.

1) CD * 3 = AJ
2) GH * 2 = JA
3) D * H = BE
4) B * H = FI

8627350941

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

1) 27 * 3 = 81
2) 09 * 2 = 18
3) 7 * 9 = 63
4) 6 * 9 = 54

A) Calculate the possible equations for CD * 3 = AJ. Eliminate any equation whose product has two digits that are the same. Eliminate any equation whose product shares a common digit with the multiplicand.
32 * 3 = 96
29 * 3 = 87
27 * 3 = 81
26 * 3 = 78
23 * 3 = 69
21 * 3 = 63
19 * 3 = 57
18 * 3 = 54
16 * 3 = 48
12 * 3 = 36
09 * 3 = 27
08 * 3 = 24
07 * 3 = 21
06 * 3 = 18
04 * 3 = 12
B) Calculate the possible equations for GH * 2 = JA. Eliminate any equation whose product has two digits that are the same. Eliminate any equation whose product shares a common digit with the multiplicand.
48 * 2 = 96
47 * 2 = 94
46 * 2 = 92
45 * 2 = 90
43 * 2 = 86
41 * 2 = 82
39 * 2 = 78
38 * 2 = 76
36 * 2 = 72
35 * 2 = 70
34 * 2 = 68
32 * 2 = 64
31 * 2 = 62
29 * 2 = 58
28 * 2 = 56
27 * 2 = 54
23 * 2 = 46
19 * 2 = 38
18 * 2 = 36
17 * 2 = 34
16 * 2 = 32
15 * 2 = 30
14 * 2 = 28
13 * 2 = 26
09 * 2 = 18
08 * 2 = 16
07 * 2 = 14
C) Pair together any two equations whose products are reversed digits.
29 * 3 = 87 and 39 * 2 = 78
27 * 3 = 81 and 09 * 2 = 18
23 * 3 = 69 and 48 * 2 = 96
21 * 3 = 63 and 18 * 2 = 36
09 * 3 = 27 and 36 * 2 = 72
07 * 3 = 21 and 06 * 2 = 12
D) Eliminate any pair of formulas where the multiplicands share at least one digit. For those remaining pairs, calculate D * H = BE.
27 * 3 = 81 and 09 * 2 = 18 and 7 * 9 = 63
23 * 3 = 69 and 48 * 2 = 96 and 3 * 8 = 24
09 * 3 = 27 and 36 * 2 = 72 and 9 * 6 = 54
E) Eliminate any trio of formulas where the third product shares at least one digit with the first two multiplicands or products. For those remaining trios, calculate B * H = FI.
27 * 3 = 81 and 09 * 2 = 18 and 7 * 9 = 63 and 6 * 9 = 54
09 * 3 = 27 and 36 * 2 = 72 and 9 * 6 = 54 and 5 * 6 = 30
F) Eliminate any set of formulas where the fourth product shares at least one digit with the first three multiplicands or products.
27 * 3 = 81 and 09 * 2 = 18 and 7 * 9 = 63 and 6 * 9 = 54

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