DISINI 2014CSMCSolution
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Find a 3-digit integer less than 200 where each digit is odd and the sum of the cubes of the digits is the original number?. The rectangle has dimensions 67
If the squares are coloured alternately black and white, as on a chessboard, then each T-piece covers an odd number of black squares, no matter how it is placed on the board.
For each choice of a tens digit, choosing the ones digit to be equal to that tens digit gives the only number that is a multiple of 11.. That is, for each possible choice of a
(Try blocking out the numbers larger than each of these to see this.) This pattern does continue since when each of these odd perfect squares is reached, the number of spaces up to
We make a table containing each of the remaining basic sub-segments, the number of pos- sible left endpoints for a sub-segment containing it, the number of possible right endpoints,
The final digit (the units digit) must equal the hundreds digit, thus there is no choice for the units digit since it has already been chosen. In total, there are 9 × 10 choices for
remaining 15 squares are to be filled in using exactly once each of the numbers 1, 2, …, 15, so that the sum of the four numbers in each row, each column and each diagonal is
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