## Mystery Number 6Logic 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?
1) Digit A is either a square number or a triangle number, but not both. 2) Digit B is either an even number or a cube number, but not both. 3) Digit C is either a cube number or a triangle number, but not both. 4) Digit D is either an odd number or a square number, but not both. 5) Digit E is either an odd number or a cube number, but not both. 6) Digit F is either an odd number or a triangle number, but not both. 7) Digit G is either an odd number or a prime number, but not both. 8) Digit H is either an even number or a square number, but not both. 9) Digit I is either a square number or a cube number, but not both. 10) Digit J is either a prime number or a triangle number, but not both. 11) A < B, C < D, E < F, G < H, I < J 12) A + B + C + D + E < F + G + H + I + J ## Answer3605891247A = 3, B = 6, C = 0, D = 5, E = 8, F = 9, G = 1, H = 2, I = 4, J = 7 1) 3 is a triangle number, but not a square number. 2) 6 is an even number, but not a cube number. 3) 0 is a cube number, but not a triangle number. 4) 5 is an odd number, but not a square number. 5) 8 is a cube number, but not an odd number. 6) 9 is an odd number, but not a triangle number. 7) 1 is an odd number, but not a prime number. 8) 2 is an even number, but not a square number. 9) 4 is a square number, but not a cube number. 10) 7 is a prime number, but not a triangle number. 11) 3 < 6, 0 < 5, 8 < 9, 1 < 2, 4 < 7 12) 3 + 6 + 0 + 5 + 8 = 22, 9 + 1 + 2 + 4 + 7 = 23, 22 < 23 A) First, determine what two subsets of numbers qualify for each digit. However, each digit can only be in one of the subsets, not both. B) Digit A can not be 0 (a leading zero is not allowed). C) Next, eliminate those numbers that do not satisfy Condition 11. Digit I can only be 4. Digit A can only be 3. Digit B can only be 6. Digit C can only be 0. D) Digit D and Digit J must be some combination of 5 and 7. Digit E can only be 8. Digit F can only be 9. Digit G can only be 1. Digit H can only be 2. E) To satisfy Condition 12, Digit D is 5 and Digit J is 7. Hide ## What Next?
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