## Massive multiplication

By David Shaw, 13 November 2019

**Difficulty: Fun**

Sienna’s teacher is writing up a wicked problem on the board. First, the teacher writes all the numbers from 1 to 99. Then they erase 10, 20, and all the other numbers that end in 0.

“Listen up!” the teacher announces. “I want you to multiply all the numbers on the board. Tell me the last digit and I’ll give you full marks on your next assignment.”

A couple of kids at the back of the class get out their calculators, but soon realise the answer is too big to fit on the screen. Meanwhile, Sienna starts raising her hand…

Can you work out what the last digit of the multiplication is?

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

## Brainteaser hint

Why not try it! Start at 1, multiply the numbers, and see if there’s a pattern in the answers!

## Brainteaser answer

When you’re multiplying lots of numbers together, you can rearrange them, and it won’t change the answer (if multiplication is the ONLY thing you’re doing).

With that in mind, you can rearrange 2 and 5, as follows:

1 x 2 x 3 x 4 x 5 x 6 x … = 2 x 5 x 1 x 3 x 4 x 6 x … = 10 x 1 x 3 x 4 x 6 x …

As 2 x 5 = 10, you’ll be multiplying by 10. And if you multiply any whole number by 10, the last digit is a zero!

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