Equal Averages

There are several different notions of average: the mean, the median, the mode and the range (see below for the definitions). If you work out each of these statistics for the set of numbers 2, 5, 5, 6, 7, you'll notice something interesting — they are all equal to 5!

Can you find other sets of five positive whole numbers where mean = median = mode = range?

How many sets of five positive whole numbers are there with mean = median = mode = range = 100?

This puzzle comes from the NRICH site.

Eggstreme

Awash with chocolate eggs and gift bags, confectionery delirium sets in and your mind starts to wander... Given you have 20 bags, what is the minimum number of eggs needed so that you have a different number of eggs in each bag? 
This puzzle and solution can be found here.
There is an interesting non-obvious (quite mischievous) solution which nicely illustrates what mathematicians can do when the rules are not overly defined.

A 13 step problem

When I go up my stairs in a hurry, I take some steps two-at-a-time. This morning, I climbed my thirteen steps in this pattern: 1, 2, 1, 2, 1, 1, 2, 1, 2. Yesterday the pattern was 1, 1, 1, 1, 1, 1, 2, 2, 1, 2. How many days do you think I can go before I have to repeat a pattern?

This is from the NRICH site.
and is referenced in this blog post from Math with bad Drawings.

Zombie Logic Puzzle