This page gets changed very slowly. There aren't any solutions on these pages, because I don't want to spoil your fun, but there are hints. You can always request them below!
The triangle shown has one obtuse angle, at the top.
Can you cut the figure, using as many straight lines as you wish,
so that all the angles are acute?
If you can, do it!
If you can't, prove it!
Click here for a hint.
What proportion of numbers contain the digit '7'?
Click here for a hint.
Prove that all 20-digit powers of two have three repeated
digits (that is, at least one digit that occurs three times, not
necessarily consecutively)
Click here for a hint.
You get these by sending me your solution, and I confirm or correct it. Honestly, it's more fun that way. Only very special pleading gets you a solution unless you've made some attempt yourself!
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