DISINI 2015CSMCSolution
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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
(a) Find five positive integers, not necessarily different, whose sum is equal to their product.. (b) Show that the problem in (a) has at least
Part marks will be awarded only if relevant work is shown in the space provided in the answer booklet.. Let A, B and C be non-zero digits, so that BC is a two-digit positive
With a given set of four digits, the largest possible integer that can be formed puts the largest digit in the thousands place, the second largest digit in the hundreds place, the
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
(For example, the digits 4 and 1 can be arranged as 4 1 or 1 4.) We then place the leftmost digit in such an arrangement as the leftmost digit of the n -digit integer (which must
If we fix any specific digit in any of the three positions, there will be exactly 81 integers with that digit in that position, as there are 9 possibilities for each of the
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
