🕰 The clock puzzle
Why time counts to sixty
Most things we measure count up to a hundred, but minutes only count up to sixty. Nearly every mistake people make with time comes from that.
Lots of things count up to a hundred and then start again.
A euro has a hundred cents, a metre has a hundred centimetres, and a test is often marked out of a hundred.
An hour only has sixty minutes.
The puzzle
After sixty marks, the hour goes up by one
Long before clocks had hands, people told the time by a shadow. Push a stick into the ground (its old name is a gnomon) and as the sun crosses the sky its shadow sweeps round a dial. To read the dial closely, they cut it into sixty marks rather than a hundred, and clock faces have been marked that way ever since.
Your turn. Drag the long hand all the way round, or tap the buttons, and watch what happens to the hour when the long hand gets back to 60.
3:05
One lap of the long hand is 60 marks. When it reaches the 60th, the hour goes up by one. There’s no such time as 1:75.
This is where people usually go wrong.
Half a metre is fifty centimetres, but half an hour is thirty minutes.
The trap
Same word, two different numbers
A metre is 100 cm, so half a metre is 50. That makes half an hour sound like 50 minutes, but an hour is 60, so half of it is 30. Half of a metre and half of an hour come out as different numbers because a metre and an hour count up to different totals.
Before you tap: is a third of an hour a whole number of minutes? Is a third of a metre a whole number of centimetres? Make a guess, then pick a fraction and check.
Half a metre is 50 cm, but half an hour is 30 min.
People chose sixty for time instead of a round hundred for a good reason.
Sixty can be shared out in far more ways than a hundred can.
Why sixty
Sixty can be shared out in more ways than a hundred
Sixty can be split into whole minutes in far more ways than 100 can: halves, thirds, quarters, fifths and sixths all work. The people who cut the first dials chose 60 on purpose, so anyone could share an hour without messy fractions. Before you tap, guess which splits won’t work for a pretend hour of 100 minutes.
Both come out whole. 100 can be halved too, so keep going. Thirds are where it goes wrong.
Doing the sums
Adding time: you carry at sixty
Adding and taking away time works like ordinary sums, except that you carry at 60 instead of 100. Set a time, add or take away some minutes, and you’ll see the wrong answer crossed out next to the right one.
Sixty isn’t only used on clocks.
You’ll find it in lots of other places in your day.
People have counted in sixties for four thousand years, and your phone still does.
Where else sixty turns up
Sixty is still used today
The Babylonians counted in sixties thousands of years ago, and people kept using it because it can be shared out in so many ways. You’ll find it in a circle, in a second, and in the way your phone works out where you are. Tap one to see where the sixty comes in.
Where’s the sixty? Tap one:
Time counts to sixty for a good reason.
Sixty can be shared out in more ways than any smaller number.
People chose it thousands of years ago so that an hour could be split in lots of ways and still come out in whole minutes. Every clock you’ll ever read is still marked in sixties.
One more thing
If someone tells you half an hour is 50 minutes, you can show them it’s 30: an hour counts to 60, so half of it is 30, and there’s no 1:75 on any clock. You can also tell them why people picked 60 instead of a hundred: halves, thirds and quarters of 60 all come out as whole numbers. There are sixty seconds in a minute too, and a full circle is six sixties. If you can explain why it’s 30, you’ve got it.