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?
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?