Henry Ernest Dudeney/Puzzles and Curious Problems/147 - Blindness in Bats/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $147$

A naturalist was investigating (in a tediously long story) whether bats are in fact actually blind.

He discovered that blindness varied.

Two of his bats could see out of the right eye,

just three of them could see out of the left eye,

four could not see out of the left eye,

and five could not see out of the right eye.

He wanted to know the smallest number of bats that he could have examined in order to get these results.

The puzzlingly obvious solution is $7$.

One is left wondering whether this is a trick question, but no.

There must be at least $7$ bats, because they can be partitioned in $2$ ways::

with or without sight in the right eye

with or without sight in the left eye.

Both of these lead to $7$ bats.

That these conditions can be fulfilled by $7$ bats, let us suggest:

$2$ bats can see out of both eyes

$1$ bat can see out of the left eye but not the right

$4$ can not see out of either eye

and the conditions are consistent.

$\blacksquare$