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

From ProofWiki
Jump to navigation Jump to search

Puzzles and Curious Problems by Henry Ernest Dudeney: $237$

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:

\(\text {(1)}: \quad\) \(\ds 3 d\) \(=\) \(\ds p + 150\) They found that if they set up the posts $1$ foot asunder they would have too few by $150$.
\(\text {(2)}: \quad\) \(\ds d\) \(=\) \(\ds p - 70\) But if they placed them a yard asunder there would be too many by $70$.
\(\ds \leadsto \ \ \) \(\ds 2 d\) \(=\) \(\ds 220\) $(1) - (2)$
\(\ds \leadsto \ \ \) \(\ds d\) \(=\) \(\ds 110\)
\(\ds \leadsto \ \ \) \(\ds p\) \(=\) \(\ds 110 + 70 = 180\) substituting from $(2)$

Hence the result.

$\blacksquare$


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Henry_Ernest_Dudeney/Puzzles_and_Curious_Problems/237_-_The_Mudbury_War_Memorial/Solution&oldid=640905"