Brain Teasers
Super - Crazy Math Squares
Place 16 different 2-digit numbers in a 4x4 square grid so that they add up to the same number horizontally, vertically, and diagonally, and horizontally, vertically, and diagonally when turned UPSIDE - DOWN.
Hint
This is not a trick question.The magic sum is 264.
Answer
The numbers should be like this:96 11 89 68
88 69 91 16
61 86 18 99
19 98 66 81
*Note that the only numbers used are 1, 6, 8, and 9, because these numbers can be read as either the same or a different number when turned upside down.
Example: 1 and 8 look the same upside down, but 6 turns into 9 and 9 turns into 6.
So 89 becomes 68, 99 becomes 66, etc., and the numbers in the box still add up to 264 (vertically, horizontally, and diagonally) upside down!!
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Comments
I was thinking other digits would work, too. 2 becomes 5 (digital display), 5 becomes 2, 3 stays as 3.
So don't use 4 or 7. Would that be the only restriction?
So don't use 4 or 7. Would that be the only restriction?
3 doesn't stay at 3.It becomes E.
88 88 88 88
88 88 88 88
88 88 88 88
88 88 88 88
Where doe sit say that they have to be different?
88 88 88 88
88 88 88 88
88 88 88 88
Where doe sit say that they have to be different?
nice comment _numpty_
Mine says "different"... perhaps it was edited?
Nice puzzle, thanks.
I managed to solve it with scip (a linear, mixed integer and nonlinear programming solver). I uploaded the model file that I used to pastebin for anyone who might be interested to play with it.
http://pastebin.com/rnUxGyik
I managed to solve it with scip (a linear, mixed integer and nonlinear programming solver). I uploaded the model file that I used to pastebin for anyone who might be interested to play with it.
http://pastebin.com/rnUxGyik
Modifying a little bit the scip model parameters I found out that
the 1x1 puzzle has 4 solutions (11,69,88,96)
the 2x2 puzzle has no solutions
the 3x3 puzzle has no solutions
the 4x4 puzzle has 1152 solutions
the 1x1 puzzle has 4 solutions (11,69,88,96)
the 2x2 puzzle has no solutions
the 3x3 puzzle has no solutions
the 4x4 puzzle has 1152 solutions
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