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Quote:

In 1882, AmerIcan chess player and puzzle writer Samuel Loyd issued a challenge to the public worth $1,000 (which is $22,727.27 USD today ). Out of several million answers, only two were found to be correct. Give it a try, show how to arrange the seven figures and the eight “dots”—.4.5.6.7.8.9.0.—to add up to 82.

Solution:

A dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc). With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc). The remarkable feature here is that a proper fraction divided by 9s (eg. 46/99) is exactly equal to the numerator with the repeater sign followed by the decimal. So, as per the mathematical truths above, one solution is : 80 + .55.... + .9797.... + .4646.... = 80 + 55/99 + 97/99 + 46/99 = 80 + 198/99 = 82).