Blog

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!

 

brain icon

Brainteaser hint

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

brain icon

 

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!

For more brainteasers and puzzles for kids, subscribe to Double Helix magazine!

Subscribe now! button

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

By submitting this form, you give CSIRO permission to publish your comments on our websites. Please make sure the comments are your own. For more information please see our terms and conditions.

Why choose the Double Helix magazine for your students?

Perfect for ages 8 – 14

Developed by experienced editors

Engaging and motivating

*84% of readers are more interested in science

Engaging students voice