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Dear Mitch,

I teach an Enrichment Math class for 6th grade girls in a private school in NJ.  I gave them your "Chanukkah Candle Question" which was a good challenge question for them.  I printed out the answer to hand out to the class but I think there are some mistakes in the calculation.  

I got percentages that were just 1 to 2 pennies off for Nights 4, 5, & 6.  

The cost for Night 3: 1.44 x 4= $5.76,  

NOT $5.67, 

And the cost for Night 6 (I had $2.50 x 7), but using your $2.52 x 7 we got $17.64,

NOT $15.34.  

The TOTAL that I got is $106.39 based on $1.73 for Night 4, $2.08 for Night 5, and $2.50 for Night 6. 

I look forward to hearing from you.

Shira Gross

New Jersey


Dear Ms. Gross.

THANK YOU for taking the time to write in. 

You are 100% correct on each and every one of the eight corrections on my calculations.  I always appreciate being corrected, and although we do most of our responses in private emails (or the site would be uselessly cluttered in no time), I decided to post yours as one of the week's publicly 'aired' letters.


  1. So I can publicly demonstrate to the young intern responsible for this one that it is actually important to check one's work?

      Or . . .

2. To demonstrate that this is the type of question that can elicit a range of different but equally valid solutions?

                   No, and No. 

On this one, there is no intern to 'blame'; unfortunately, I did all the 'work' myself, and the mistakes are mine. 

And, of course, this problem is NOT the type that is known to have different but equally valid answers – or, to the extent that it does have some room for differences, the numbers I presented would still be WRONG.  When we consider the opportunities in the question to round a little so that we don't end up with the absurd result of having to 'cut' pennies into fractional pieces, one can end up with answers that are a few cents different.

Often, there is the possibility of correctly rounding different ways, depending upon the tools we use and the method best suited for those tools.  For example, when I am working on something where people are going to rely upon my answer to make important decisions (such as for their family or for the health and safety of others), I tend to use fractions.  Why?  Because the decimals that calculators round to are not as perfect as the simple fractions they are trying to describe.  (FOR EXAMPLE, 1/3 becomes .3333, and that can lead to bigger and bigger inaccuracies as you plug sets of such numbers into formulas.     

As a teacher, there are a few answers I would accept as correct for this one, and mine would certainly not be among that group of correct responses.

When I saw your letter and gleaned it involved possible 'mistakes', I turned away from the screen and did what I often recommend colleagues do:  Simply reread the original problem and do it again.  (Often a lot simpler and faster than searching through a pile of  one's own scribbles hoping to spot mistakes.) 

And --your class should be proud to hear -- this time I rounded each price to the exact ones you used, and I ended up with your correct answer.  I also redid the previous set of calculations and you were right on each and every count.

Originally, I am ashamed to say, I did all of the arithmetic in my head while walking my dog, and only later, when we got home, did I manage to write down what I thought I remembered.  

This time, I used a pencil and paper and wrote everything down.

I tell that story not to blame the dog, but to emphasize the risk one takes when not approaching ANY task with enough attention to detail. 

Again, thank you for taking the time to suggest I check my work.  It makes a difference.

Finally, since you are (at least to my knowledge) the first one to catch something like this since we 'launched' one year and one week ago, I, on behalf of, will be sending your class a pretty cool gift.  However, please be patient; we probably will not get caught up with our shipping until after the holiday break. 

May You Continue to Shed Light During this Holiday Season,

And for Many, Many More in the Future

-- Mitch