13.4 The most popular Monthly problem 407
13.4 The most popular Monthly problem
The following problem, E 1111, is said to be the most popular problem in
theAmerican Mathematical Monthly. It was proposed by P. L. Chessin
and appeared in the April issue of 1954.
Our good friend and eminent numerologist, Professor Euclide
Paracelso Bombasto Umbugio, has been busily engaged test-
ing on his desk calculator the 81 · 109 possible solutions to the
problem of reconstructing the following exact long division
in which the digits indiscriminately were each replaced byx
save in the quotient where they were almost entirely omitted.xx8xx
xxx)xxxxxxxx
xxx
xxxx
xxx
xxxx
xxxxDeflate the Professor! That is, reduce the possibilities to(18·
109 )^0.Martin Gardner’s remark: Because any number raised to the power
of zero is one, the reader’s task is to discover the unique reconstruction
of the problem. The 8 is in correct position above the line, making it
the third digit of a five-digit answer. The problem is easier than it looks,
yielding readily to a few elementary insights.