Henry Ernest Dudeney/Puzzles and Curious Problems/7 - Squaring Pocket-Money/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $7$

A man has four different English coins in his pocket,

and their sum in pence was a square number.

He spent one of the coins, and the sum of the remainder in shillings was a square number.

He then spent one of the three, and the sum of the other two in pence was a square number.

And when he deducted the number of farthings in one of them from the number of halfpennies in the other, the remainder was a square number.

What were the coins?

The solution given by Dudeney:

The coins were a half crown, a shilling, a sixpence and a penny ($49$ pence).

He spent the penny, and the number of shillings was then $4$.

He then spent the shilling, and the number of pence was $36$.

And as the half crown equals $60$ halfpence, and the sixpence equals $24$ farthings, their difference is $36$ -- again a square.

One suggestion is that the coins were a groat, two threepenny bits and a sixpence.

However, it may be assumed that the groat is disallowed on account of it not being legal tender at the time of writing this puzzle.