Here is the question that my child was assigned as extra credit work at school:

What is the product of all whole numbers less than 100 whose names (in English) contain a subset of the letters e, f, g, h, i, t, n, r - with no letter appearing more than once per number.

Can anybody help with this question? Please!

lanaharman@msn.com

LAST EDITED ON Dec-13-01 AT 04:23 PM (EST)
 
> What is the product of all whole numbers less than 100
>whose names (in English) contain a subset of the letters e,
>f, g, h, i, t, n, r - with no letter appearing more than
>once per number.
>
> Can anybody help with this question? Please!
>

Keep this between us, for your child or any body else who gave a fleeting thought to the problem must be able to come up with the fact that the "teen" numbers are out of consideration because of the presence of double "e". For the same reason, "eleven" and "twelve" are also out.

Form a table with the words "one", "two", ..., "nine" in the left column and the words for tens ("twenty", ..., "ninety" ) in the top row. Put a cross into a table cell which does not satisfy the problem's condition. E.g., "thirty three" does not. See what remains. Consider the captions separately.

When finished, see what cells remain empty, take the product of the corresponding numbers.

From 1-10, only one,two,four,five,six,eight and ten fits the criteria and the 'teens' are cancelled out.

From twenty to thirty nine, all are out and forty,forty one and forty six fits. Sixty,sixty one and sixty four are the only ones fitting then on with eighty and eighty four as the last numbers before hundred to fit in.

Jerry

Whole number include the number zero. The product is not very difficult, you don't even have to know any of the other numbers.