Question

Dear Mitch,

I believe that last year at this time you started posting some Hanukkah and Christmas questions that teachers and homeschooling parents could print out for their students or children.  Do you plan on doing that again this year?  (I am a middle school teacher, and my sister is homeschooling her three children in another state, and I can tell you that we both appreciated the problems you presented.  So if you're still deciding about this, and you're counting votes, count us in!!)

Thank you for last year's, and both my sister and I are hoping on being able to thank you again for doing it again this year.

Warmest wishes for a happy and healthy holiday season,

Marilyn F.

(Also, on behalf of my sister, Constance, thank you for considering this letter.)

Answer

Dear Marilyn F. and Constance,

Yes, of course!  And now is as good a time as any!

So here are a couple to get us started (but check in frequently, as we will do our best to keep them coming throughout the holiday season, and we will attempt to divide the problems up as evenly as we reasonably can between the two holidays you mentioned).

And warmest wishes to the two of you as well!,

- Mitch

P.S. I hope you like them:

1. For its Hanukkah display, a pet store decided to fill a large fish tank with water, and then each day of the holiday add one fish to the tank to honor the eight days of the holiday.  The employees decided to use the tiniest fish they could obtain, so that the customers would have a fun challenge spotting and counting the aquarium's increasing population with the passing of each day of the 8-day holiday.  (In fact, the fish they selected were so tiny that  their combined volume on the eighth and final evening was so small compared to the tank's capacity as to be considered mathematically insignificant, leaving the sole challenge to be the initial filling of the tank with water.) Fortunately, the store had two pipes which were each as effective when used together as they would have been if used separately.  If one of the pipes could fill the tank in 1 1/2 hours, and the other pipe could fill the tank in 45 minutes, how much time do you think it took for the two pipes to fill the tank when the employees used the pipes together?

(A) 1 1/2 hours

(B) 1 hour

(C) 5/6 hour

(D) 1/2 hour

(E) 1/3 hour

2. In a group of  50 students, 29 celebrate Hanukkah, and 36 celebrate Christmas. If every one of the students in the group celebrates Hanukkah or Christmas or both Hanukkah and Christmas, how many of the students celebrate both holidays?

(A) 10

(B) 11

(C) 12

(D) 13

(E) 14

(F) 15