Henry Ernest Dudeney/Puzzles and Curious Problems/237 - The Mudbury War Memorial/Solution

by : $237$

 * The Mudbury War Memorial
 * The inhabitants of Mudbury recently erected a war memorial,
 * and they proposed to enclose a piece of ground on which it stands with posts.
 * They found that if they set up the posts $1$ foot asunder they would have too few by $150$.
 * But if they placed them a yard asunder there would be too many by $70$.
 * How many posts had they in hand?

Solution
They had $180$ posts.

The memorial ground was $110$ yards, that is $330$ feet, around.

Proof
Recall there are $3$ feet to the yard.

Let $d$ yards be the length of the perimeter of the war memorial ground.

Let $p$ be the number of posts they have.

We have:

Hence the result.