Henry Ernest Dudeney/Puzzles and Curious Problems/249 - Odds and Evens/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $249$

Place eight counters in a pile on the middle circle so that they shall be in proper numerical order, with $1$ on the top and $8$ on the bottom.

It is required to transfer $1$, $3$, $5$, $7$ to the circle marked "Odds", and $2$, $4$, $6$, $8$ to the circle marked "Evens".

You can only move one counter at a time from circle to circle, and you must never place a number on a smaller number,

nor an odd number and an even number together on the same circle.

What are the fewest possible moves?

The fewest possible moves are as follows, given by ordered pairs of the letters identifying the circles from and to which the counters are moved.

$\tuple {E, A}, \tuple {E, B}, \tuple {E, C}, \tuple {E, D}, \tuple {B, D}, \tuple {E, B},$

$\tuple {C, B}, \tuple {A, B}, \tuple {E, C}, \tuple {E, A}, \tuple {B, A}, \tuple {C, E},$

$\tuple {B, C}, \tuple {A, C}, \tuple {B, A}, \tuple {C, B}, \tuple {C, A}, \tuple {B, A},$

$\tuple {E, C}, \tuple {E, B}, \tuple {C, B}, \tuple {D, E}, \tuple {D, B}, \tuple {E, B}$

That is, $24$ moves.