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Dear Mitch,

Thank you for posting that Halloween problem-solving puzzle with the scales.

My classes and I are having great fun with it!

You mentioned that you would post the answer by Halloween, so I was wondering, is it possible to post it before the school day begins (Eastern Standard Time)?

Keep in mind that Halloween falls on a Friday, and the students won't be back until Monday.


Ms. B

Middle School Math Teacher

Burlington, VT


Dear Ms. B.,

Thank you for sharing your enthusiasm!

I must say, I have been pleasantly surprised by the response to this one. We've received enough emails with questions about it or students' attempts at answers to place it in the top ten or fifteen of all the problems and questions we've posted since beginning this site, almost two years ago!

For those who missed this one or are tuning in for the first time, the text to the question can be found on the October 28th Q&A in the archive, which is "The Long-awaited Halloween Super-challenge is Here", and the diagram that goes with it (which is the most important part) can be found from that October 28th Q&A; all you have to do is click on the q&a on the upper right-hand side of it that says 'Monster Math for Halloween', and scroll down to the bottom. Once you do that, the picture of the four balance scales with monsters, skulls, bats and pumpkins is hard to miss!

For now, though, here's what I'm going to do:

I am returning all emails from people asking for the solution (including you, of course!) but I am doing it in private emails.

Here, on the website I will post a very helpful hint in time for all students and parents to pull it up the moment they walk into schools, regardless of their time-zone. (Even for our friends visiting the site from international time-zones!).

Then, I will post the full answer and explanation publicly in time for all students and parents to see it the moment they arrive in school on Monday morning. I think that's the best approach, and I hope it satisfies most visitors. Keep in mind, all anyone has to do to see the entire answer is write in to, and I will send the answer and explanation to them right away via personal email.

O.K., now, there are many ways to approach the problem, and so there are many ways that I could provide a hint. Anyway, here's one:

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:

1 'bat' = 2 'green monsters' PLUS (+) 1 'pumpkin',

OR ...

2 'bats' = 4 'green monsters' PLUS (+) 2 'pumpkins'.

Hope this helps,