Henry Ernest Dudeney/Puzzles and Curious Problems/343 - Tom Tiddler's Ground/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $343$

I am on Tom Tiddler's ground picking up gold and silver.

Here we have a piece of land marked off with $36$ circular plots,

on each of which is deposited a bag containing as many sovereigns as the figures indicate in the diagram.

I am allowed to pick up as many bags of gold as I like,

provided I do not take two lying on the same line.

What is the greatest amount of money I can secure?

These are contained in $10$ bags, all deposited on the outside plots, thus:

$4$, $5$ and $6$ in the first row

$5$ in the second row

$4$ in the third row

$3$ in the fourth row

$5$ in the fifth row

$5$, $6$ and $4$ in the bottom row.

Total: $47$.

If you include $5$ bags containing $6$ sovereigns each, you can get only $9$ bags and so a value of $46$ sovereigns.

$\blacksquare$