June 12, 2007

Mathematical games for Ice Breaker

The objective of the game is to use a quick demonstration to attract and focus the group's attention on you and the presentation to follow.

Ask for a volunteer to assist you. Explain that you are going to foretell the results of a math exercise. Position yourself any place where you cannot see what the person is going to write. Ask the volunteer to write on the flipchart, chalkboard, etc., any 3 digit number. (The number must not be a mirror image, e.g., 232, 446.) Then tell the person to reverse the number and subtract the lower number from the higher one; for example: 935 - 539 = 396. Now reverse this number and add it to the preceding product to obtain: 396 + 639 = 1089.

As the volunteer completes the calculation, hold up a prepared card on which you had previously written the number 1089.
This exercise will always result in the number 1089. On occasion, the initial subtraction will yield a 2 digit number, simply direct the volunteer to add a zero in front of the number.

Why is this always equal to 1089?

This is one of the better tricks of its kind, because the effect of reversing the digits is not obvious to most people at first... If the 3-digit number reads abc, it's equal to 100a+10b+c, and we have the following result after the second step:

| (100a+10b+c) - (100c+10b+a) | = 99 | a-c |

The quantity | a-c | is between 2 and 9, so the above is a 3-digit multiple of 99, namely: 198, 297, 396, 495, 594, 693, 792 or 891. The middle digit is always 9, while the first and last digits of any such multiple add up to 9. Thus, adding the thing and its reverse gives 909 plus twice 90, which is 1089, as advertised.