Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. Try lots of examples. What happens? Can you explain it?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
What is the sum of all the digits in all the integers from one to
Watch the video to see Charlie's number trick.
If you can't play the video, you can read a description here.
Try a few examples for yourself. Do you always get a multiple of 11?
Can you explain why?
Alison and Charlie came up with their own explanations:
If you can't play the videos, you can read a description here.
Here are some similar number tricks.
Can you use Charlie's or Alison's representation to explain how they work?
Once you've been able to explain what is going on above, you should be able to explain why many other similar tricks work.
Here is a selection you might like to try:
Think of Two Numbers
Puzzling Place Value