How many numbers with a 5?

Quicky:
How many numbers between 1 and 999 contain a 5?

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Two watches

I started two watches at the same time and found that one went two minutes an hour too slow and the other one minute an hour too fast, so that when I looked at them again the faster one was exactly one hour ahead. Can you figure out from from the picture at what time before noon the watches must have started?

This problem was first posted by American puzzle genius Sam Loyd. It was incorporated into his Cyclopedia of Puzzles on page 30.

You can check your solution here

You are welcome to remark on the quirks in the puzzle, and i especially welcome your solution times. The solutions itself will be published after one week.

Five triangles

Imagine a right triangle (formerly called a rectangled triangle). One side adjacent to the right angle is twice as long as the other. You will not find it very difficult to construct a square from 4 of these triangles.

But is it possible to construct a square from 5 of these triangles? And from 6? From 7?

These problems are derived from ‘doordenkertje’ 12 in the November 1969 issue of ‘Pythagoras’, a Dutch magazine in recreational mathematics. You will need some elementary geometry knowledge to solve this problem.

You can check your solution here