Patrick Vennebush shared this puzzle from his new book, One-Hundred Problems Involving the Number 100:

It’s easy to cover a hundred chart with 100 small squares: 10 rows of 10 squares = 100.

It’s easy to cover a hundred chart with one big square: one 10×10 square = 100.

But can you cover the chart with 20 squares? Or with 57 squares? The squares do NOT have to be all the same size.

If we only consider squares with whole-number sides, so they exactly fit on the grid, then:

- What numbers of squares work to cover the chart?
- What numbers don’t work — and can you prove it?

Click to read the original puzzle along with some teaching tips at Patrick’s blog:

If you’d like some printable hundred charts for coloring in squares, download my free *Hundred Charts Galore!* file from my publisher’s online store:

And discover more ways to play with these printables in my classic blog post: 30+ Things to Do with a Hundred Chart.