I think 28 too.

Bob

]]>I looked at the upper left-hand side only.

H

HT

HTA

HTAM

In this part, there are 2^3 paths which produce MATH, because, at every letter we can either go up or right, and there are 3 places where we make the choice.

It's the same for the other 3, so it's 32 total, but, because we counted each straight path twice, we subtract 4 to get the number of possible ways to spell MATH to be 28.

I'd say 28 is correct.

]]>Draw the grid and letters and write a 1 over the M. There's only one M so all routes start there.

Now go to an A. There are 4 of these so write a 1 over each. (see picture)

Now to go to a T. I've just shown the ways to get to one of the Ts. You can go up then right, or right then up so I've written a 2 over that T. Do the same for the other Ts.

Now how can you get to an H from a T? Work that out and write the correct number over each H. Add them up and there's your answer.

EDIT: I'm getting a lot more than 16.

Bob

]]>But a cursory examination yields at least 16 so I would think 12 is incorrect.

]]>Thanks

]]>How many Distinct paths can be followed to spell the word **MATH**