# Magic Mind Reader

*Material Required: Chart-paper, pen, cutter.*

Here is a simple game to boggle your mind. Cut out seven cards from chart paper in equal

sized rectangles (about “8 x 6”). On the main card copy out the numbers 1 to 20. On the remaining 6 cards, cut windows in the pattern shown in the figure and also copy down the numbers on the bottom two rows of each card. Now the game is ready.

Ask your friend to think of a number from the main card. Let her/ him tell you on which of the other six cards (mask cards) the number appears. There will be three cards on which it appears. Stack these three cards together and place it on the main card aligning the edges. The number your friend thought of appears in the magic window!

How does it work?

There are six mask cards. Any three of them contain a given number. The different ways in which you can select three cards out of six is given by the formula:

There are twenty different ways of selecting 3 cards out of six. So you can have twenty different numbers shown within the magic window which shifts with each combination of 3 cards. Look in the main card and you will find that there are twenty numbers, exactly ^{6}C_{3. }The windows have to be cut on each card so that each combination of 3 cards gives a unique window. This can be done by copying the pattern in the figure or by trial and error.