Did you solve it? Are you smarter than a weather forecaster?

Today I set you the following puzzles about the weather.

1. The weather forecast

It is raining at midnight. Will we have sunny weather in 72 hours?

Solution. No! In 72 hours it will be midnight and the sun will have set.

(Unless you are reading this from inside the Arctic or Antarctic circles. If you are, please tell us more in the comments below.)

2. Stripy socks

Wind socks show wind direction. But why are they usually striped?

Solution: In order to show the speed of the wind. When there is no wind, the sock droops down. As the wind increases, the sock becomes horizontal. The number of stripes visible in the part of the sock that is horizontal is an indication of wind speed. Each visible stripe (before the sock droops) is supposed to represent 3 knots.

3. Windy Wendy

Wendy cycled 10 miles in 30 minutes with the wind in her back. When she returned against the wind, the trip took 40 minutes.

On a windless day, how long would it take her to cycle 10 miles?

Solution About 34.3 minutes.

There are various ways to solve this. Here’s one way. Ten miles in 30 minutes is 1/3 miles per minute. Ten miles in 40 minutes is 1/4 miles per minute.

We can rephrase theses speeds as 8/24 and 6/24 miles a minute. The windless speed must be half way between, since the wind either makes you go faster, or slower, by the same amount. Thus the windless speed is 7/24 miles a minute. Since speed = distance/time, the time = distance/speed, which is 10/7/24 = 240/7 = 34.2857

4. Barometer brainstorm

A weather forecaster’s favourite instrument is the barometer, which measures air pressure. According to urban legend, a physics professor once asked his students how to measure the height of a building using a barometer.

The obvious answer is to measure pressure at the bottom and the top: the change in pressure can be used to deduce the relative altitudes. But that wasn’t the answer he was looking for. He wanted more inventive solutions. As do I.

How might you use a barometer to measure the height of a tall building?

I asked you to post your suggestions below the line. (Click here to return to that post.) Possible answers include:

• Throw it off the top and time how long it takes to reach the bottom

• Measure its shadow, and compare to the shadow of the building

• Give it as a gift to someone who knows the answer already, such as the architect or building manager.

Please keep on adding new ideas.

I hope you enjoyed today’s puzzles. I’ll be back in two weeks.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.