Guess What ?? [Answered]

Dec 17 2011

by Abdullah Najuib

Answer

8274965103

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

1 ) A = 8 (I < J)
2 ) B = 2 (J < A)
3 ) C = 7 (A > B)
4 ) D = 4 (B < C)
5 ) E = 9 (C > D)
6 ) F = 6 (D < E)
7 ) G = 5 (E > F)
8 ) H = 1 (F > G)
9 ) I = 0 (G > H)
10 ) J = 3 (H > I)

Brute force methods can be used to arrive at a solution. However, process of elimination does work. For example, assign 8 to H. I can not exceed H, so J would have to be 3 (8 already assigned to H). G can not exceed H, so I would have to be either 6 or 7. I would be greater than J, so A would have to be 7 (3 already assigned to J), meaning I would have to be 6. J is less than A, so B would be 2 (3 already assigned to J). A is greater than B, so C would be 5 (7 already assigned to A). The only remaining numeral for G is 0, which means F would have to be greater than G, meaning H would have to be either 1 or 4. H has already been assigned 8, rendering that assignment impossible. Continue eliminating possibilities in the order shown below.

A) H can not be 8. C can not be 1. C can not be 0. B can not be 9. D can not be 1. D can not be 2. F can not be 1.
B) H must be 1. H can not be 4. H can not be 9.
C) G can not be 0. I can not be 6. I can not be 7. B can not be 0.
D) I must be 0. I can not be 8.
E) J can not be 2. J can not be 5. J can not be 8.
F) J must be 3. A can not be 3. B can not be 3. E can not be 3.
G) B must be 2. F can not be 2.
H) A must be 8. A can not be 4. A can not be 7.
I) D can not be 9.
J) E must be 9. E can not be 5. E can not be 6.
K) D must be 4. F can not be 4.
L) F must be 6. G can not be 6.
M) G must be 5. C can not be 5. G can not be 5.
N) C must be 7.