Question

Dear Mitch,

For the last few weeks I noticed you've been answering requests for Thanksgiving Maths problems, especially targeted at what you refer to in America as the 'middle school level'. I'm a Maths teacher who happens to teach at the British equivalent of your 'middle school level', and I teach at an international school that acknowledges all foreign holidays in addition to the ones of Britain. Your 'Thanksgiving' is an important one for our school community, so I for one appreciated the problems and ideas you shared!

What I was wondering is if now, with the American Thanksgiving behind us, would you be willing to try to hit some of the other major holidays like that? If so, the next major one coming up that we celebrate in our school is Hanukkah, which this year begins about one week from now. After that, of course, is Christmas. Even a few problems for each holiday that are different from the basic ones I find on other websites would be appreciated. In fact, anything along the lines of what you did for your Thanksgiving would be perfect!

Thank you,

Mr. Ronaldson,

Manchester, United Kingdom

Answer

Dear Mr. Ronaldson,

Of course!

In fact, as you might know if you've been reading posts on this website with regularity, I not only spend as much time as I possibly can in your beautiful country, but I actually have family in London!

Hanukkah Math:

There is, as you will see if you glance around the internet, a very old and well-known Hanukkah word problem that has been given to children for as long as I know, and that certainly included the time of my own childhood. So, just to be thorough, we might as well begin with that before we step things up to make them a bit more interesting than what everyone else posts.

Here is the problem:

There are eight nights of Hanukkah, and candles are lighted on each of the eight nights. There is one extra candle each night, called the "shamus" or 'helper' candle, and that one is lighted first, and the others are lighted from it.

The pattern is this: Night 1 of Hanukkah: One candle plus the helper candle (or two altogether).

Night 2: Two candles plus the helper candle (or three altogether)

And so on...

Until the last night of the holiday, on which eight candles are lighted plus the one helper candle (or 9 altogether).

Now, it is important to note that the candles used for this holiday are special candles designed for this purpose, and they burn down fairly quickly, with the idea that no one has to go to sleep at night worrying about a candle still burning and, for example, falling and beginning a disaster.

No, they finish burning and are cold long before bedtime.

BUT, because of this feature, it has become an important tradition not to interfere with the light by ever intentionally blowing any of the candles out. So, each candle that is used from the beginning of the holiday to the end is a new one, including the 'helper candle', which is also a new candle each night. And the set of candles for the holiday usually come boxed together in one small package.

And the question is this:

Altogether, how many candles does a family need to celebrate the entire holiday lighting the appropriate number each night?

And that comes down to a series of relatively easy addition problems, which is really just one big addition problem. (I would recommend against allowing calculator use on this simple one; it is good practice of very basic skills).

Now, for what one of my colleagues would call the 'Mitchellistic" follow-up to this straightforward question:

If one family has adapted its own private tradition for embellishing the usual Hanukkah candle-lighting procedure, and they like to buy their candles separately so that they can locate and purchase fancier and fancier candles as the holiday progresses, so that with each night they step things up to a slightly grander scale, and they use the same number of candles as everyone else celebrating, but with candles that are priced this way:

Each night of the eight nights the candles they use are 20% more costly than the candles of the preceding night.

How much will that tradition cost the family if the first night's candles cost $2.00 for the pair?

Happy Holidays, and Good Luck!

Oh, I'll post the answer in a day or two (unless other teachers write in that they'd rather I hold off a little longer, as sometimes is the case).

Hope this helps,

Mitch