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use the numbers 0-9 so that each row and column =20
diagonals are not included

--- --- 8 4
9 --- --- 4
7 --- 3 ---
--- --- --- ---


which one dosen't belong and WHY...
36, 163, 68, 960, 1661, 62

the fact that 1661 has 4 digits dosen't count

2007-10-16 13:50:34 · 2 answers · asked by ? 1 in Science & Mathematics Mathematics

2 answers

PROBLEM 1:

This is a little like Sudoku. Let's use letters in the blank spaces so I can explain each step. Also, I assume that they mean you must use the values 0 through 9 *exactly once* in the blanks (otherwise this is trivial)

A B 8 4
9 C D 4
7 E 3 F
G H J K

We know that A+G = 4. They can't both be 2 so:
A could be 0, 1, 3 or 4
G could be 0, 1, 3 or 4

Next A+B = 8, using the values above:
B could be 4, 5, 7, 8, but 4 isn't allowed because A and B can't be the same.
Thus:
A could be 0, 1 or 3
B could be 8, 7 or 5
G could be 4, 3 or 1

E+F = 10
E is 1,2,3,4,6,7,8,9
F is 9,8,7,6,4,3,2,1

F+K = 12, so the only possible values of K (excluding duplicates):
K = 3,4,5,8,9
But now F can only be:
F = 9,8,7,4,3
And E can only be:
E = 1,2,3,6,7

C+D = 7
C is 0,1,2,3,4,5,6,7
D is 7,6,5,4,3,2,1,0

D+J=9, and since D is 0 through 7
J is 2,3,4,5,6,7,8,9

A B 8 4
9 C D 4
7 E 3 F
G H J K

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

Time to try some values... if we assume A=0, then B=8 and G=4. That limits our choices for E, F and K. That then drives our values for C, D and J...

Oh heck, here's the answer I came up with. It uses 0 through 9 exactly once in the blanks. I don't know if it is the only answer, but it is an answer.

(0)(8) 8 4
9 (5)(2) 4
7 (1) 3 (9)
(4)(6)(7)(3)

PROBLEM 2:

The answer is obviously 36 if you just look at the tens digit (all the rest are 6)

2007-10-16 14:35:04 · answer #1 · answered by Puzzling 7 · 0 1

3584
9344
7364
1928

I assume we could use a number more than twice in a row/column because you had the two 4s right next to each other.

1661 because it is a palindrome (number or word that reads the same frontwards as backwards ex. kayak, level, 1234321, 579975)

2007-10-16 14:02:42 · answer #2 · answered by Anonymous · 0 0

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