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Question

Dear Mitch,

Can you post another one of those balance-scale problems for the Christmas season?

(But a different one than the one you posted last Christmas because my teacher already pulled that one up and she loves it so I wanted to surprise her with a new one.)

Thank you,

J. Bartlett

Answer

Dear J. Bartlett,

Yes, and here they are!

Below, you will find a new Christmas challenge problem of the type you mention, as well as a Hanukkah one that is exactly as challenging, but, of course, with a different 'theme' to it.

Hope you enjoy them, and happy holidays!

Mitch

 

 

CHRISTMAS BALANCE

A series of weighings is shown below. The items on the scales are small ornaments for a family's Christmas tree.  There are three different kinds of ornaments – glass candy canes, tiny porcelain snowmen, and miniature Christmas trees. 

Going from top to bottom, the first two scales (scale A and scale B) are balanced and complete.

But the third scale (scale C) is not.

QUESTION:  How many Christmas trees will have to be ADDED to the five snowmen on the right-hand side of scale C in order to form a balance with the left-hand side of that scale, which, as depicted in the illustration, is holding 5 glass candy canes?

Christmas Hanukkah Math Challenge

 

 

 

HANUKKAH BALANCE 

A series of weighings is shown below. The items on the scales are small ornaments for a family's Hanukkah celebration.  There are three different kinds of ornaments – dreidels, which children spin to play games, candles, which are lighted each night of the holiday, and presents for the children.

 

Going from top to bottom, the first two scales (scale A and scale B) are balanced and complete.

 

But the third scale (scale C) is not.

 

QUESTION:  How many of the presents will have to be ADDED to the five candles on the right-hand side of scale C in order to form a balance with the left-hand side of that scale, which, as depicted in the illustration, is holding 5 dreidels?

 

Christmas Hanukkah Math Challenge