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, L987, 5s. 41/2d., 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
reader find this last form?

91.--MORE MIXED FRACTIONS.

When I first published my solution to the last puzzle, I was led to
attempt the expression of all numbers in turn up to 100 by a mixed
fraction containing all the nine digits. Here are twelve numbers for the
reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72,
94. Use every one of the nine digits once, and only once, in every case.

92.--DIGITAL SQUARE NUMBERS.

Here are the nine digits so arranged that they form four square numbers:
9, 81, 324, 576. Now, can you put them all together so as to form a
single square number--(I) the smallest possible, and (II) the largest
possible?

93.--THE MYSTIC ELEVEN.

Can you find the largest possible number containing any nine of the ten
digits (calling nought a digit) that can be divided by 11 without a
remainder? Can you also find the smallest possible number produced in
the same way that is divisible by 11? Here is an example, where the
digit 5 has been omitted: 896743012. This number contains nine of the
digits and is divisible by 11, but it is neither the largest nor the
smallest number that will work.

94.--THE DIGITAL CENTURY.

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