Problems

One of your employees insists on being paid daily in gold. You have a gold bar whose value is that of seven days’ salary for this employee. The bar is already segmented into seven equal pieces. If you are allowed to make just two cuts in the bar, and must settle with the employee at the end of each day, how do you do it?

You have a 3-quart bucket, a 5-quart bucket, and an infinite supply of water. How can you measure out exactly 4 quarts?

Suppose you had eight billiard balls, the recruiter began. One of them is slightly heavier, but the only way to tell is by put-ting it on a scale against the others. What’s the fewest number of times you’d have to use the scale to find the heavier ball?

How many times a day do a clock’s hands overlap?

How do you cut a rectangular cake into two equal pieces when someone has already removed a rectangular piece from it? The removed piece can be of any size or orientation. You are allowed just one straight cut.

Why does a mirror reverse right and left instead of up and down?

Remove a \(1 \times 1\) square from the corner of a \(4 \times 4\) square. Can this shape be dissected into \(3\) congruent parts?

Max asked Emily how old she was. She replied that she was 13 years old the day before yesterday, and will be 16 next year. Then, Max asked her brother, whether it was true, and he said yes. How is it possible if nobody was lying?

Place coins on a \(6\times 6\) chequered board (one coin on one square), so that all the horizontal lines contain different number of coins, and all vertical lines contain the same number of coins.

A big square was cut into smaller squares. Sebastian used all the pieces and constructed two squares with different side lengths by glueing the pieces together. Show an example of how he could do that.