## The difficult dial

By David Shaw, 4 September 2019

While working on an old weaving machine, Aisha spied a dial that needed repairing.

The dial had numbers counting upwards, evenly spaced around the outside. Although she couldn’t see the whole dial, she could see that the number 6 was directly opposite 17.

Can you work out how many numbers there are on the dial?

Scroll down for the answer!

## Brainteaser answer

If the numbers are evenly spaced, there will be the same amount between 6 and 17, whichever way you go.

There are ten numbers between 6 and 17, so there must be ten between 17 and 6. Adding in both 17 and 6, there must be 22 numbers in total!

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25 November, 2019 at 9:36 pm

0 is a number. most dials start at 0. so there are 6 numbers below the 6, and 6 numbers above the 17.

so the biggest number is 23.

therefore there are 24 numbers

26 November, 2019 at 10:07 am

Hi Simon,

Starting at zero is a good point! but I don’t think you’re right.

You have to turn the knob 11 notches to get from 6 to 17 in ascending order. since the two numbers are directly opposite, you need to pass the same number of notches if you turn the opposite way too.

starting at 6, we turn 11 notches and end on 17:

5, 4, 3, 2, 1, 0, 21, 20, 19, 18, 17.

So the largest number is 21, and there are 22 numbers on the knob!

28 November, 2019 at 10:24 pm

sorry , you are right. i went the wrong direction!!