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To view the notebooks you'll need
the LiveMath plug-in, found at Weigh Godzilla! Things really get interesting when you choose your own weights in a two-pan balance scale. Just highlight the right-hand sides of A through J, below, and type your own positive integer value. However, you must arrange your values of A through J in nondecreasing order, meaning that your weights do not have to be distinct (see below). Use the Delete key (not the Backspace key) to remove unwanted digits from the weights you enter. The important thing is this: Some choices of weights cannot weigh every integer-weighted object in its range, i.e., less than or equal to the sum of all the weights. If your choice of weights is defective, that is., if it violates a certain necessary and sufficient condition, Godzilla will offer you friendly notification of this fact. Godzilla's weight will automatically be set equal to a value that is impossible to weigh given your choice of A through J. You will never be able to make the scale balance in this case. This time, you must do the checking that any letter on the scale appears at most once. Godzilla can only tolerate one friendly reminder.
Original mathematical design © 2003 by Dean Clark |