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Dear Mitch,

I am a rabbi/teacher, who would like to share some information, and then ask if you could come up with a mathematical puzzle that I could present this coming week to classes in a high school and youth group I oversee in New Jersey.

Rosh Hashanah is the holiday that marks the beginning of the New Year for Jewish people around the world.  On the standard calendar used in the United States, the exact date of this holiday differs slightly from year to year, as do most Jewish holidays, because their dates are determined by a much older calendar, which began recording time over five thousand years ago, rather than 2009 years ago.  This year, the Rosh Hashanah holiday, which is always celebrated for two days, begins on the 19th of September and extends through the 20th of September.  Like most Jewish holidays, though, its observance and celebration begins at sundown the night before the first day, making the evening of September 18th "Rosh Hashanah Eve".


Three of the traditional symbols for this holiday are apples, honey, and something called a "shofar".  The apples are sliced and dipped in the honey and enjoyed as part of the festive meal to symbolize the sweetness of beginning a new year and, in particular, the sweetness anticipated in the year to come.  The "shofar" is a ram's horn; a "ram" is a male goat, and for thousands of years this type of horn was sounded by being blown (similar to the way a bugle is blown) to produce a rich, unique sound that can, when done with enough focused energy and practice, be heard about a mile away from a mountain top.  Its powerful sound welcomes in the New Year with gusto.


Thank you for posting this on your site (assumming you do), and thank you for keeping your site going for the young people (and not so young, like myself).  I know that many people in my community visit this site regularly.




Rabbi Jacob Greene



Dear Rabbi Jacob Greene,

First, thank you for your kind words.  Second, here goes:

Below is a mathematical puzzle using depictions of the three symbols mentioned above (apples, honey, and shofars).


As you can see, the first two scales (Scale A and Scale B) are perfectly balanced.  Scale C, however, is not yet balanced. 


QUESTION:  Based upon what you can learn and figure out from the two balanced scales (Scale A and Scale B), how many jars of honey would you need to put on the tray on the right-hand side of Scale C in order to form a perfect balance with the left-hand side of Scale C, which, as shown, is holding one apple and one shofar?


(For the purposes of this puzzle, you can assume that each apple in Scale AScale B, and Scale C are of equal weight, and each jar of honey depicted (and any jar of honey which you can use to balance Scale C) weighs the same amount as any other jar of honey depicted in the puzzle.  Also, of course, each shofar (ram's horn) is of identical weight to any other shofar depicted in this puzzle. HAVE FUN... AND GOOD LUCK PROBLEM-SOLVING!


-- Mitch