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Amusements in Mathematics by Henry Ernest Dudeney
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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.

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