Question

Dear Mitch,

I'm sure other people have already bothered you about this, but you assured the visitors to your website that by the Monday morning following Halloween you'd post the answer to the super-challenge Halloween problem with the balance scales that has all the students (and a lot of the teachers) talking. You were right; it is certainly a perplexing one! 'And since you mentioned it is the kind more popular in Asian Math curricula, it's no wonder those kids seem to become the wizards we often hear about.

Looking forward to having the answer by tomorrow morning when I get up before sunrise to do my prep for the day's classes,

Miss Catton,

Middle School Math Coach

Woonsocket, RI

Answer

Dear Miss Catton,

First, just in case someone missed it and still wants to give it a try (though most people seem to feel it's almost impossibly challenging), the necessary illustration of the four balance scales can be found at the bottom of the recent q&a with the word Halloween in it, and by clicking the 'Monster math' link at the top, or something like that, and one can find the text to the question in the other Halloween Q&A. Though, really, all one needs to do is find the image of the four scales, which was in one of the last few q&a's, print it up, and know this:

After looking at the first three balance scales, you can use the knowledge they reveal to balance the fourth scale. On that one, the fourth scale, you need to balance the skull using ONLY green monsters on the other side.

SO, NOW THAT THAT'S OUT OF THE WAY...

AS PROMISED, HERE GOES:

THE ANSWER IS:

5 Green Monsters!

How?

Look: In order to make the two left sides of scales A and B equal, add 1 green monster to each side of scale B. This means that 1 bat equals 2 green monsters + 1 pumpkin.

(Or):

2 bats equal 4 green monsters + 2 pumpkins.

Scale C shows that 2 bats also equal 3 pumpkins,

(Or):

4 green monsters + 2 pumpkins equal 3 pumpkins.

Now, subtracting 2 pumpkins from each side, we find that the weight of 4 green monsters equals the weight of 1 pumpkin.

Next, we exchange the 1 pumpkin in scale B with 4 green monsters -- and so we can...

Balance the SKULL in SCALE D with 5 GREEN MONSTERS.

Hope you and your classes had fun with this, and I hope this helped,

Mitch