Numbers with Divisible Digits
How many 4 digit positive integers have the ones digit a multiple of 1, the tens digit a multiple of 2, the hundreds digit a multiple of 3 and the thousands digit a multiple of 4?
Details and assumptions
The number is a two digit number.
The answer is 400.
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1 solution
Any digit is a multiple of 1, so there are 10 possible unit digits. There are 5 digits that are multiples of 2, (2,4,6,8,0), so there are 5 possible digits for the tens place. There are 4 digits that are multiples of 3, (3,6,9,0), so there are 4 possible digits for the hundreds place. There are 3 digits that are multiples of 4, (4,8,0), but in order to be a 4 digit number, we cant start with 0, so there are 2 possible digits for the thousands place. By the rule of product, there are 1 0 × 5 × 4 × 2 = 4 0 0 such numbers.