Henry Ernest Dudeney/Modern Puzzles/143 - The Stone Pedestal/Solution

by : $143$

 * The Stone Pedestal
 * In laying the base and cubic pedestal for a certain public memorial,
 * the stonemason used cubic blocks of stone all measuring one foot on each side.
 * There was exactly the same number of these blocks (all uncut) in the pedestal as in the square base on the centre of which it stood.
 * Look at the sketch and try to determine the total number of blocks actually used.


 * Dudeney-Modern-Puzzles-143.png


 * The base is only a single block in depth.

Solution

 * $1458$ blocks.

Proof
Ridiculously messy question.

Let $2 x$ be the number of blocks used in total.

Then we have that $x$ are used in the base and $x$ are used in the pedestal.

Let $y$ be the number of blocks on along one edge of the pedestal.

We have that:
 * $x = y^3$

It looks as though the length of one side of the base is $3$ times the length of one edge of the pedestal.

On that assumption, we have that: