1610.11 – One Million
Find two whole numbers whose product is 1,000,000 but neither of the two numbers has any zeros in it.
Discussion: The whole point of this simply-stated problem is to show the value of making simpler versions of it.
Solving the Problem: How about using 10 instead? That's easy: . OK, how about 100? , or .
Oh. So . So . . . 1,000,000 is , and there we are: . Who'd a thunk it?
Heuristic: #14, make a simpler version, big-time.
Using the Problem with Students:
a. as a class activity. We look at the problem together. In good Stella style, it seems hopeless at first. I don't like to spend a lot of time on this one, so I suggest right away that students think of an easier number than 1,000,000. They'll fumble around and I'll keep at them until somebody sees that 10 is a good way to start. Then we quickly go on from there until the solution pops out.
Another way is to do a prime factorization of 1,000,000. It comes down to all 2's and 5's. Lump the 2's together and lump the 5's together and you have it.
Similar Problem: 1180.822: tennis tournament (also in this intro set)