The number 24 is a multiple of 6, and its reversal, 42, is also a multiple of 6.
What is the probability that the reversal of any randomly-chosen multiple of 6 is also a multiple of 6?
Intuitively I believe the answer is 4/9.
A number is divisible by 6 iff it's divisible by 2 and 3. A number is divisible by 3 if the sum of its digits is divisible by 3; therefore reversing a number's digits doesn't change its divisibility by 3.
We only have to check, then, if the reverse is divisible by 2. The last digit of the reversed number will be an integer from 1-9, pretty much uniformly randomly I believe. So there's a 4/9 chance that the reverse is divisible by 2 and therefore divisible by 6.
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Posted by tomarken
on 2024-02-22 07:04:47 |
Solution?
