# What's new ## Numbers and letterboxes

, 11 July 2018

Tomas is putting a number on a letterbox.

He puts on one digit.

Then he adds another digit. Tomas looks at it and notices that it makes a number exactly five times the first digit.

Tomas adds a third and final digit. Once again, Tomas looks at the number and notices that the three digit number is five times the previous two digit number.

What number is written on the letterbox? If you think about the question, you might notice a few helpful clues.

One clue is where to add the extra digits. If you stick the second digit after the first, you’ll get a number that’s more than 10 times larger than the original! This is too big, so the second digit must come before the first.

Another clue is that the two digit and three digit numbers must both be multiples of five. That means the last digits of both must be 0 or 5.

Combining these two clues, the first number written down must be a 0 or a 5.

If we try 0, then we can calculate the next number: 5 x 0 = 0. This might make sense – we could write this as 00. Following this idea through, we get a three digit number: 000. It’s not something you’d regularly see on a letterbox, but it’s a possible answer.

If we start with 5, we get a different solution. 5 x 5 = 25, so the second number Tomas wrote was a 2. And finally, 25 x 5 = 125, so the last number he wrote is 1. Finally, just to check, 125 is a very reasonable number to find on a letterbox.

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