## Mystery Number 4Logic puzzles require you to think. You will have to be logical in your reasoning.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 ## Answer8627350941A = 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 Hide ## What Next?
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