Now that we have looked at the Gauss Trick, we would like to see why it works. Mathematicians do this sort of thing to see whether a trick like this will work in more complicated situations. So we will ask a few true-false questions to see if you can figure out why it works.

? True False  1. To find the sum using the Gauss trick, we always multiply the column sums by 1 more than the larger number and then divide by 2

? True False  2. To find the sum using the Gauss trick, we always multiply the column sums by the difference between the largest and smallest number and then divide by 2

? True False  3. The Gauss Trick will only work when the column sums (that is, the sums of the pairs consisting of a number in the first line and the number below it in the second line) are all the same number

? True False  4. The Gauss Trick will only work when the differences between consecutive numbers being summed is the same

? True False  5. To find the sum using the Gauss trick, we always multiply the column sums by the number of numbers being summed and then divide by 2

? True False  6. The Gauss Trick will only work when the numbers being added are consecutive (that is, we do not skip any numbers between the first and the last.)