## Which bus?

By David Shaw, 13 June 2018

I caught a bus the other day with a very interesting number. Can you work out the number on the bus?

- It has four digits
- It’s less than 2000
- Its digits add up to 10
- If you reverse its digits, you get the same number (it’s a palindrome)

Scroll down for the answer!

## Brainteaser answer

The bus I caught was number 1441.

Here’s one way to work it out:

- If it has four digits and it’s less than 2000, the first digit must be a 1.
- Since it’s the same forwards and backwards, the last digit must also be 1.
- Since all the digits together make 10, the middle two digits must add to eight.
- Since the number is the same forwards and backwards, the two middle digits must be the same, so they must both be 4.

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15 June, 2018 at 1:58 pm

I came up with 0550 which fits the bill except that it ends up having a leading zero, so I guess it’s not truly a four digit number. Bummer.

15 June, 2018 at 2:31 pm

Hi Greg,

I like your answer! Actually, I had a look around on the internet and found a bus with a leading zero:

https://www.123rf.com/photo_94740610_rostov-on-don-russia-january-2018-a-small-hyundai-bus-rides-along-route-number-40-through-the-street.html

So I reckon your answer is perfectly good!

16 June, 2018 at 10:36 pm

Look up the history of the number zero, very interesting. Both as a concept and a number. Greg is 100% right. A 4 digit number can most certainly begin with a zero as 0000 is a valid 4 digit number, just not a correct answer to this brainteaser. 0550 and 1441 are correct answers.

17 June, 2018 at 12:10 am

https://www.sciencedaily.com/releases/2018/06/180607141031.htm