FALLACIES 141

horse (on paper only). This made the total of horses eighteen
instead of seventeen, and of this new total:

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These are the respective shares for the three sons, and these
shares total 17 (i.e. 9+6+2), leaving the borrowed horse to
be ‘paid back’.

It is to be noted that each son receives a fraction of a horse
more than his entitlement, because the father bequeathed
less than his full possessions. This explains the apparently
fallacious argument that all three sons may receive their full
legacies and yet leave the borrowed horse to be returned to |
its owner. The bequests were 1-+21+41 and these total
only #1ths of the 17 horses. The extra ‘parts’ received by
each son are in proportion to his legacy. 4 has half a horse
extra; B has an extra third and C has an extra ninth of a
horse.

This problem is not confined to the numbers used above,
but may be posed and solved by the same method where other
numbers are involved. If, for example, there were 19 horses
to be divided amongst 4, B and C in the proportions, one-
half, one-quarter and one-fifth, we can, by adding 1 to the
total, divide the new total into the required amounts and
still have the extra horse left over afterwards. The new total
would be 20, and these would be distributed as follows:

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Remainder

There are many similar examples.

Fallacies usually arise in numbering because of mis-
interpretations of the meanings of certain algebraic or purely
numerical identities, but nowhere is there likely to be greater
misinterpretation than in the construing of statistics.

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