快猫短视频

#100 Late for the gate

This deceptively tricky everyday problem set in an airport was first posed by the US mathematician  in 2008.

You are in a bit of a rush to catch your plane, which is leaving from a remote gate in the terminal. Some stretches of the terminal have moving walkways, or travelators, and others are carpeted. You always walk at the same speed, but travelators obviously boost this.

You look down and spot that your shoelaces have come undone. This won鈥檛 slow you down, but it is annoying, so you decide to stop to tie them. It will take the same amount of time to tie your laces if you are on the carpet or on the travelator, but if you want to minimise the time it takes you to reach the gate, where should you tie your laces?

#99 Around the clock

Solution

It is 2 o鈥檆lock. We don鈥檛 know how many numbers are in the right position, but we are told that if we did know this, we could work out the time.

There are several orientations in which no number is in the right place. If just one number is in the right position, it could be 1, 3, 6 or 10. If three are in the right position, then those three might be 4,9,11 or 5, 7, 12. However, if two are in the right place, those numbers can only be 2 and 8.

The hour hand is pointing at 2 which is in the correct position, so the time is 2 o鈥檆lock. If the pranksters have painted XI and IX upside down, there is still only one pair of numbers that could be in the correct position.