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#31 Fold and cut

set by Katie Steckles

Imagine a piece of paper in a portrait (or vertical) orientation. If you want to make this puzzle more challenging, this imaginary piece of paper is all you need, otherwise, you can always try with a real one.

If you fold the paper in half twice (first down, then across), and then cut a small piece off each corner, how many holes will you make through the paper?

What about if you make three folds (down, then across, then down) before snipping the corners off? How many holes now?

Is there a connection between the number of folds and the number of holes?

Solution next week

#30 Digital targets

Solution

The optimal set of numbers is 1, 2, 3, 4, 5, 0, 0, 0, 0 and 0. This gets 150 points.

The digits 0, 1, 1, 2, 3, 4, 5, 9, 9 and 9 can be arranged several ways to get a score of 100 – for example, as 14, 19, 29, 39 and 50.

The highest possible score with the digits 0-9 is 95. There are many ways to arrange this – for example: 19, 28, 37, 46 and 50.