# Just showing off some math…

Even though I am not eligible (I don’t think) to win Monday Math Madness, since I already won this year, I will continue submitting solutions (since they are fun).

And? They liked my solution to #25, and printed it.

The contest is over, but here’s the question:

A number is considered to be monotonically increasing if each digit is greater than the one preceding it. For example, 24579 is monotonically increasing but 24559 is not (the 4th digit is not greater than the third digit) nor is 24759 (the 4th digit is not greater than the third digit.)

If you randomly select a number between 1 and 1,000,000 what is the probability that the number will be monotonically increasing? Assume that all single-digit numbers are monotonically increasing.

While you are welcome to write a computer program to verify your answer, to be eligible for a prize you must demonstrate how to solve the problem without use of a computer.

Originally published at Wild About Math.

That’s a nice solution, and I like it all the more because it’s exactly the one I came up with too (I hadn’t seen the puzzle until now). Pretty!

So I had a student today ask me if I could come up with a simple 2 dimensional area problem. I was like -sure what is it. The question was:

If a cow were strapped to a tether outside a 10′ by 10′ square barn, at the corner of a small outlet door, and had a 100′ leash/tether, what would the area be that he could cover to graze?

So the obvious is a circular sweep CCW with a 100 square foot keep out area in one direction, but then other? any ideas how to compute this one? thanks newbie