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

by : $147$

 * Blindness in Bats

Solution
The puzzlingly obvious solution is $7$.

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

Proof
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.