GeekDad Puzzle of the Week Solution – Pirate Booty

This past week’s puzzle as posted on International Talk Like a Pirate Day:

Pirate Captain Max, First Mate Nora, and two o’ their buccaneer buckos stumbled upon some pirate treaaye. Specifically, they found a bejeweled necklace o’ 31 gemstones. After findin’ its value, they picked t’ gemstones one at a time (Max, Nora, Buccaneer 1, Buccaneer 2, etc.) with each pirate pickin’ t’ largest stone left, until all t’ stones were taken. Based upon t’ observations below, how much was t’ necklace worth, and how much booty did each pirate get?

• The largest Ruby is 80% the value of the smallest Topaz, its neighbor.
• The largest Emerald is worth $2,000 less that the smallest Ruby, to which it is immediately adjacent.
• Each successively smaller Sapphire is worth only half of its neighbor.
• There are a total of three Topaz stones.
• The more expensive Sapphire is worth $10,000.
• The difference between the two adjacent Sapphires on each side is $1000.
• Each successively smaller Emerald is worth only 80% of its larger Emerald neighbor.
• The central Topaz is most valuable stone.
• The largest Sapphire is the value of the abutting smallest Emerald, rounded down to the nearest $1000.
• Each of the two smaller Topaz stones are worth 6 of the larger’s pieces of 8 or 6/8.
• The number of Amethysts and the number of Sapphires (combined) sum to the number of Emeralds.
• The largest Amethyst is worth only half of its neighbor, the smallest Sapphire.
• There are two fewer Amethysts than there are Rubies.
• Each successively smaller ruby is worth $1,000 less than its predecessor.

Of the several submissions sent, the most popular method used to solve the puzzle above was simple algebra. Starting on one side of the symmetric necklace, there were 3 Amethysts, 2 Sapphires, 5 Emeralds, 4 Rubies, 1 Topaz and then the central Topaz. This makes for a total of 3 Topaz, 8 Rubies, 10 Emeralds, 4 Sapphires, and 6 Amethysts.

Broken out by individual stone, it looks like this:

If Max selected the most valuable stone (central topaz) first, Nora the second most valuable, etc., their totals work out to be:

Congratulations to SAnderson for correctly answering the puzzle and having their response drawn at random from the set of reasonably correct submissions to win this week’s $50 ThinkGeek Gift Certificate.

Happy puzzling!