When the three digits of a three-digit number N are multiplied together, the result is a two digit number obtained by removing the middle digit of N. Find all such numbers N

thanks you very much

Printable View

- June 7th 2005, 01:28 AMChuck_3000**Please Help!!!* *
When the three digits of a three-digit number N are multiplied together, the result is a two digit number obtained by removing the middle digit of N. Find all such numbers N

thanks you very much - June 7th 2005, 06:55 AMhpeQuote:

Originally Posted by**Chuck_3000**

The two digit number made from a and c is 10a + c, so the condition you are interested in is

Solve for a:

Now c = 1,2,3,...,9, so for b = 1, a would have to be negative. Thus b=1 is impossible.

The idea then is to look at all larger values of b and try values of c such that this fraction is an integer between 1 and 9.

For b>1, we must have

which leads to

So for b = 4, e.g., we only need to look at c = 1, 2,3.

Using this information and trying all cases, you can find the solutions is reasonable time. I found four solutions. - June 16th 2005, 05:17 PMchuri55
135, 162, 234, 326

is what I obtained using Maple...great piece of software!