It is another good puzzle so to arrange the nine digits (the nought
excluded) into two groups so that one group when divided by the other
produces a given number without remainder. For example, 1 3 4 5 8
divided by 6 7 2 9 gives 2. Can the reader find similar arrangements
producing 3, 4, 5, 6, 7, 8, and 9 respectively? Also, can he find the
pairs of smallest possible numbers in each case? Thus, 1 4 6 5 8 divided
by 7 3 2 9 is just as correct for 2 as the other example we have given,
but the numbers are higher.


89.--ADDING THE DIGITS.

If I write the sum of money, £987, 5s. 4½d., and add up the digits,
they sum to 36. No digit has thus been used a second time in the amount
or addition. This is the largest amount possible under the conditions.
Now find the smallest possible amount, pounds, shillings, pence, and
farthings being all represented. You need not use more of the nine
digits than you choose, but no digit may be repeated throughout. The
nought is not allowed.


90.--THE CENTURY PUZZLE.

Can you write 100 in the form of a mixed number, using all the nine
digits once, and only once? The late distinguished French mathematician,
Edouard Lucas, found seven different ways of doing it, and expressed his
doubts as to there being any other ways. As a matter of fact there are
just eleven ways and no more. Here is one of them, 91+5742/638. Nine of
the other ways have similarly two figures in the integral part of the
number, but the eleventh expression has only one figure there. Can the