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Mind Reading

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Always a Multiple?

Age 11 to 14 Challenge Level:

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?
 

  • Take any two-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?
     
  • Take any two-digit number. Add its digits, and subtract your answer from your original number. What do you notice?
     
  • Take any three-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?
     
  • Take any five-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

 
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:

Special Numbers
Think of Two Numbers
Legs Eleven
Puzzling Place Value