Divisibility...You thought it was simple???
Let be the number of different digit numbers with the digits and , no digit repeated twice and is divisible by . What is the value of ?
The answer is 192.
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1 solution
For a number to be divisible by four, the last two digits need to be divisible by 4. Given the numbers 1,2,3,4,5,6, we can create the 8 two-digit numbers 12, 16, 24, 32, 36, 52, 56 and 64. For each of these two-digit numbers, there are four remaining number (2 of the six already being chosen), of which we need three. These three numbers can appear in any order, so we have 4P3 possibilities for each of our two-digit numbers.
4P3*8
=24*8
=192 possible numbers.