Henry Ernest Dudeney/Puzzles and Curious Problems/356 - A Rail Problem

Puzzles and Curious Problems by Henry Ernest Dudeney: $356$

A Rail Problem

There is a garden railing similar to our design.

In each division between two uprights there is an equal number of ornamental rails,

and a rail is divided in halves and a portion stuck on each side of every upright,

except that the uprights at the end have not been given half rails.

Idly counting the rails from one end to another, we found that there were $1223$ rails, counting two halves as one rail.

We also noticed that the number of those divisions was five more than twice the number of whole rails in a division.

How many rails were there in each division?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Unclassified Problems: $356$. -- A Rail Problem
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $256$. A Rail Problem