Question

Dear Mitch,

A few days ago you mentioned you would be posting a super-challenge problem for this Halloween. I believe you mentioned it would be one of those balance scale types of problem-solving that are common in the Japanese math curriculum. Halloween is coming up in a few days, so do you think you'll get to it soon?

Thank you,

Mrs. B. Craft,

Middle School Math Teacher,

Chicago, IL

Answer

Dear Mrs. B. Craft,

Yes!

There was an unexpected challenge getting the image to look right, but now, thanks to my dear friend of 30 years, Patrick M., the software challenge was surmounted and it's up!

For the moment, the image can be found at the bottom of the answer to the question & answer entitled "Monster Math for Halloween", and is the q&a of October 16^{th}. It can be found by going to the top-right of this page, and clicking on "Monster Math" and then scrolling down to the bottom of that Q&A.

For the actual text and question that accompany that illustration for one of my all-time favorites, here we go:

In the illustration below, a series of weighings is shown. The first three (scale A, scale B, and scale C are balanced and complete), but the fourth (scale D) is not. The items on the scales are all Halloween decorations, and there are four types of decorations depicted: There are toy skulls, toy pumpkins, toy bats, and toy 'green monsters'.

** QUESTION**: Based on what can be learned from studying scales A, B, and C, how many 'Green Monsters' must you put on the empty side of scale D in order to balance the skull on the left-hand side of that scale?

Good Luck,

Mitch