The digits 1, 2, 5, 6, and 9 are all used to form five-digit even numbers in which no digit is repeated. What is the third-largest of these numbers?

Guest Apr 6, 2021

#1**0 **

The largest number will be the digit that starts with the largest number and goes down the chain, which would be $96521$.

But wait! They have to be even! So the largest number would be $96512$. The next largest number would use 2 as the hundreds digit, so it would be $96251$.

But wait! It has to be even again! Because we used up the 6 and the two already, we need to have 1 in the hundreds place: $96152$.

So now, our list of numbers is $96512,96152$. So the third even number would use 5 as a thousands digit, so $95621$, but that is not even! It would be $\boxed{95612}$

RiemannIntegralzzz Apr 6, 2021