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?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Can you explain how this card trick works?
When the pack has been shuffled and then split, let us assume
that there are x cards face up in the pile of 20. This
being the case, there must be 20 - x cards face up in the
second pile. When the pile of 20 is turned upside down there will
be 20 - (20 - x) = x cards face up in the pile.
Therefore both piles of cards will have the same number of cards (
x ) face up.
Of course the trick works just as well if the volunteer chooses
25 cards or any other number of cards. You might like to convince
yourself that this is so by rewriting the above solution replacing
20 by 25.