You may also like

problem icon

Calendar Capers

Choose any three by three square of dates on a calendar page...

problem icon

Card Trick 2

Can you explain how this card trick works?

problem icon

Happy Numbers

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.

Card Trick 1

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.