Friday Puzzle -- powers of 3

correction

Alex Y

I'm sure you understood the point, but just in case, the second sum I wrote does not add to 100. change one of the "1"s to a "9", and it would make the point I was trying to demonstrate--the order of the addends does not matter.

Re: correction

bill earl

I resisted the urge to code this up. But sketching it out on paper, it looks like Clementine's dad.

Re: correction

bill earl

Maybe not. Looks like I pushed more than I popped & wound up off by a right-angle. I should know better than to attempt recursion manually - on a Friday afternoon no less.

If that's an answer

Alex Y

you've totally lost me! I, too did it manually (as long as you allow Excel as a "notepad" for listing solutions and also allow it to check them). But my answer bore no relation to 49 or 90 or 139, which are the only answers I came to with these hints.

But then again, you are usually two steps ahead of me in your allusional answers!

Re: If that's an answer

Larry Barrett

I come up with 401.

Hard to keep track of the various combinations, but here is what I have:

Using just 1s, there is 1 way to get to 100.

Using at least 1 3 and 1s there are 33 ways to get to 100.

Using at least 1 9 and various combinations of 3s and 1s, there are 176 ways to get to 100.

Using at least 1 27 and various combinations of 9s, 3s, and 1s, there are 179 ways to get to 100.

Using 81 and various combinations of 27s,9s, 3s, 1s there are 12 ways to get to 100.

You are a lot closer than I was

Alex Y

I had about 370. But I like your organization of the problem. Using a spreadsheet to impllement your approach, I came up with all the same numbers, but one. I had 180 as the number of combinations with 27 as the highest power of 3 (12 combos with 3 27s, 51 with 2, and 117 with 3). So 402 as total.

The place I saw this puzzle still has "Answer to be posted soon" on the web site, so I'll have to confirm the answer later, along with a more elegant solution if there is any.

Nice solution.

Re: You are a lot closer than I was

Larry Barrett

I agree with you; I had the same results for the 3 27s combos and the 2 27s combos, but was off by 1 for the 1 27 combos. There are patterns to the combos, but not so easy to write down in a simple form.