Tuesday, May 19, 2009

Light Humor and More on a Math Puzzle

We all need a break from the seriousness of math, so here are some (actual) amusing headlines. Before I get nasty comments, remember these are real!

1. Teachers Strike Idle Kids
2. Eye Drops Off Shelf
3. Miners Refuse To Work After Death
4. Hospitals Are Sued By 7 Foot Doctors
5. British Left Waffles On Falkland Islands

Ok, enough of the silliness...

I received several emails and comments about the math puzzle from the other day. Essentially, they all indicated that the problem was readily solved using technology.

First, here is the solution:
123456789 = 10821 x 11409

Aniket S., a computer science major from Solapur University, India, sent me the solution and the code she used in C++ to find the factors.

Both Mike Croucher and Pat Ballew, who emailed me, used the powerful new computing engine Wolfram Alpha to find the factors. As Pat pointed out, "the times they are a changin'...

In fact, I found the prime factors of 123456789 on the TI-89:

factor (123456789)
3^2 x 3607 x 3803

A few additional thoughts...
Is there anything special about the number 123456789? If we randomly permute the digits to, say, 586421739, we obtain the prime factorization 3^2 x 107 x 608953, which cannot be rearranged to form two 5-digit factors due to the 6-digit prime. Can you find a permutation of 123456789 which can also be factored into two 5-digit numbers?

If we make one change to the original number we can solve the puzzle:
123456784 = 10406 x 11864.

Have fun computing...

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