### Brain Teasers

# Mystery Number 4

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

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

### Answer

8627350941A = 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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