Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat this for a number of your choice from the second row. You
should now have just one number left on the bottom row, circle it.
Find the total for the three numbers circled. Compare this total
with the number in the centre of the square. What do you find? Can
you explain why this happens?
Can you explain how this card trick works?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
In general, if a and b are single digits and
a > b , ba becomes ab .
Between the two numbers ab and ba there is a
10 ( a - b ) + ( b - a )
= 10 a - 10 b - b - a
= 9 ( a - b )
So to turn ab into ba do the following
ba = ab - 9 ( a - b )
Alternative solution - can you justify it?
Add the digits, multiply by 11 and then
subtract the original number.
Correct solutions to this problem were
received from: Archbishop Sancroft High School; Stephen and
South Greenhoe Middle School; Jack, Paul and
Matthew - Smithdon High