# Five numbers with median and mean

5 distinct integers between 1 and 10, inclusive are chosen. Their median is 4 and their mean is 3.6. What are the numbers?

• An idea here might be to at least leave open how many numbers there are in total. This still makes for a very easy solve, but is arguably a tiny bit more compelling Commented Aug 2 at 13:30
• That's a good idea, but it's too late to change it, because we have an accepted answer that assumes 5 numbers. Commented Aug 2 at 14:31
• +1 An enjoyable simple puzzle. Commented Aug 2 at 19:00
• Thank you @Will.Octagon.Gibson. Now you can try this one: puzzling.stackexchange.com/questions/127682/… Commented Aug 3 at 4:24

## 1 Answer

For a mean of 3.6 from five numbers, we need a sum of 18.
So we need a sum of 14 from the remaining four numbers.
To make 4 the median, we need two numbers on either side of it. So two of them must be larger and are at least 5+6 = 11.
That leaves at most 3 for the sum of the two smaller numbers and everything is forced.

The numbers are 1, 2, 4, 5, 6.

• Yep you got it! Good explanation. Commented Aug 2 at 11:48