Geekdad Puzzle of the Week Solution: Are You Smarter Than a Ferengi Third Grader?

Welcome back, my crazed calculating comrades! Did you figure out this week's puzzle? I'm not sure how a Ferengi third grader solves a problem like this, but a human GeekDad relies on his lifelong companion: algebra.

Puzzle:

A merchant has a necklace made up of 33 gems worth 65,000 bars of gold pressed latinum.The biggest and most expensive gem is right in the middle of the string of gems. The individual gems start with the cheapest ones at each end. From one end the gems increase in value by 100 bars of gold pressed latinum up to and including the big gem. From the other end the gems increase in value by an even 150 bars of gold presses latinum up to and including the big gem. How much is the largest gem worth?

Solution

Now some of you used brute force and Excel to plug-and-pray a solution. Others probably used some type of scripting program to hammer out a solution. Then some of you, and you know who you are, warmed my heart by using our old friend algebra. Here's the solution using nothing but pen and paper.

The necklace has 16 Gems on each side of the big gem.

Let n be the value of the first gem on the left side then n + 100 is the second gem n + 200 is the third etc. The total value of the left had side is then 16n + 12000

Let m be the value of the first gem on the right hand side. Then m + 150 is the second gem , m + 300 is the seconf etc. The total value of the right hand side is 16m + 18000

That gives a formula for the necklace value as 16n + 12000 + 16m + 18000 + Big Gem = 65000
That reduces to 16n + 16m + Big Gem = 35000

Now we also know the following

Big Gem = n + 1600
Big Gem = m + 2400

This leads to n + 1600 = m + 2400 .... or n = m + 800

We can now express this equation 16n + 16m + Big Gem = 35000 in terms of m and solve for m

16(m + 800) + 16m + m + 2400 = 35000
16m + 12800 + 16m + m + 2400 = 35000
33m + 15200 = 35000
33m = 19800
m = 600
So the Big Gem = 600 + 2400 = 3000 bars of gold pressed latinum

There you have once again algebra to the rescue. Only thing left to do is announce the winner of this week's $50.00 ThinkGeek gift certificate. The winner is Tony, who correctly solved the puzzle and beat the odds to win this week's prize! For those of you who didn't win use this code GEEKDAD72JL and get $10.00 of your next order of $50.00 or more at ThinkGeek.

Come back Monday when Gareth returns with a new puzzle. I can hear him laughing maniacally as he works on it in his cubicle ... actually he always laughs maniacally. It's kind of creepy.