Here is a new brain teaser from puzzle master Wes Carroll. He found this one in the Mensa publication Number Puzzles for Math Geniuses by Harold Gale.
Tipping the Scales
Question:
The top two scales are in perfect balance. How many diamonds will be needed to balance the bottom set?
This puzzle works your executive functions in your frontal lobes by using your pattern recognition, hypothesis testing, and logic.
Click here to read the Answer and Solution.
How about if we just add spades to the right?
Counting the number of spades is part of it, but you have to know the proportion of spades, clubs, and diamonds to each other to solve the problem.
This is easy if you aren't overly smart, you just count the items and add. If you use higher mathematics, it's probably more difficult.
I agree with Amber. If we only add more spades, we'll need some fractions.
Aside from the fractions, the question asks "How many diamonds will be needed to balance the bottom set?". So you have to add diamonds not spades.
What you see on the first two balance scales is all you have to deal with, just use 'em all up and you can't go wrong.
Exactly!
a culb is worth 7 points, a spade 3 and a diamond 5, now do the math!
[...] 17. What about Tipping the Scales. [...]
Need 4 more Diamonds!
Try to add scale #1 plus scale #2 together...
:D
its 4 diamonds i belive look at the top one theres 1 diamond and 3 spades= 2 clubs so take three spades out of the bottom scale and take 2 clubs out and add a diamond. now theres 3 clubs and 2 spades on the bottom scale now look at the middle scale its 3 diamondsand 2 spades = 3 clubs u already have the beggining of that on the bottom scale now, just add 3 diamonds and its balanced, so in order to balance the bottom scale (with out takeing anything off) you need 4 diamonds
I used a series of formulas with three variables and came up with 4 diamonds. However, just adding the scales probably would have worked hahaha.
Great work, David.
[...] [...]
I did the same as david and just added scales 1 and 2. No need for formulas lol.
4 diamonds
Dangit. Again, I went the long way. Oh well, at least I got to practice my algebra. Haven't used that in a while.
I too used higher algebra to solve the problem. I got the correct answer but it took way too long. I wonder why I didn't think of the short method in the beginning.