## When clock hands meet brainteaser

By David Shaw, 24 August 2022

**Difficulty: Fun**

For an entire day, Ruth watched a dial clock, looking for when the hands met. She wrote down all the times they met in a digital way, 4:22 for example.

When she looked over her notes, the hands met in every hour of the clock except one. Which hour did the hands not meet?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

One way to do this is by elimination. See if you can come up with examples of when the hands will meet in each hour.

Remember that the hour hand doesn’t stay still! It keeps moving throughout the hour.

## Brainteaser answer

One way to look at this problem is to look at a few meetings and try to spot the pattern.

The most obvious place to start is 12:00, where both hands point straight up. The hands next meet around 5 minutes after 1, and then about 11 minutes after 2, and so on. As we go on, the meeting happens further and further into the hour.

In hour 10, the meeting point happens just before 10:55. In hour 11, the hands get closer and closer as the hour proceeds, until they finally meet at 12:00.

Since 12:00 isn’t in the 11th hour, we’ve found our answer! The hands don’t meet in the 11th hour.

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3 September, 2022 at 10:46 am

Hi I might be reading this wrong but the way I look at it the 11th hour (11-12) ends as the two hands come together at 12. the 12 th hour starts at the fragment of time AFTER 12 and continues till 1.. and the Hands don’t meet till 105?

Am I missing something?

3 September, 2022 at 3:10 pm

Hi Allan,

That’s a perfectly good answer! I added the phrasing ‘digital’ to try and disambiguate. If you write all the meeting times out, you’ll never write 11 in the hours place. But your aswer is completely valid.

And given the weird debate about the 21st century starting in 2001, you’re probably right.