superprismatic

No, the article I referred to in the original post was talking about a different aspect of straight line programs.

Nice going, guys! If you'd like to try another, I think that 277 is pretty hard.

I recently read an article in the American Mathematical Monthly, August-September 2012, about straight line programs. The article, by Peter Borwein and Joe Hobart, was about how these things would be affected by allowing the division operation. But a rather simple idea for a puzzle formed in my head after reading it. So, here it is: A straight line program is a sequence of integers p1,p2,p3,....,pn such that p1=1 and pi is the sum, difference, or product of pk and pl where k and l are both less than i. It is OK if k=l. So, for example, one possible straight line program which ends in 12 is 1,2,4,3,12. To be explicit, p1=1, p2=p1+p1, p3=p2+p2, p4=p3-p1, p5=p4*p3. Find a shortest straight line program ending in 137.

It's provocative alright! The trouble is, I have no idea how to proceed from here. I hope you have a glimmer of an idea, Captain. By the way, I've seen this before somewhere. I think it was called Bulgarian Solitaire.

I think you're correct. In that case, I think there is only one convex solid which works -- the minimum volume is the same as the maximum volume.

It is a legal requirement in my state. I guess California is different. No. I just checked the California Motor Vehicle Code 21802 about this. It is a legal requirement even there.

Yes, those are the words in the grids. It's part of the puzzle to figure out what's going on here.

Below is a set of 10 related words which have been encripted using a letter substitution code (as in a standard cryptogram), and placed into the two small crisscross grids shown. Four words read across and six words read down. The object is to decode the grids. +TUI+T++ +O+PNOP+ +P+++P++ +++OUNOP +++++O++ +++++P++ ++C+Y +HGRB +++L+ +++B+ [/code] Here are two hints: 1. The longest word in the grid (TOPNOP), when decoded, has a second meaning having nothing to do with the other words in the grid. This other meaning could be expressed as 1/2 NOPOBUOBU + 1/2 TOPOAEB. (These words are encrypted with the same alphabet as the words in the grids.) In a very different way, TOPNOP = 1/2 TOP + 1/2 YB. 2. If the 15 different letters that appear in the decoded grid words and decoded hint words are placed in alphabetical order and then reencrypted using the same alphabet that they had been encrypted with before, they will spell a 15-letter word that appears in the English Wiktionary. Note on the origin of this puzzle: This is very nearly a verbatim statement of a contest on page 76 of the July, 2012 issue of GAMES magazine. The deadline for entering this contest (July 31, 2012) has passed.

I hope that's it because I've tried to solve this one for a looooooong time. if not, hey i tried. I like the quote though. Indeed, you've got it. Nice going!

For an integer n≥2, let On = {1,3,5,...,2n-1}. Prove that n2-2 cannot be written as a sum of distict elements of On.

I must say that the only thing that intrigued me about this puzzle was the tiling with the cards. I figured that the 40 characters revealed through the card cut-outs had to be some crazy thing to boil down to a single word. Personally, I don't enjoy working on such left-brain shenanigans. After all, I couldn't even understand Molly Mae's explanation of the oh-mega-puzzle-1 solution. That's definitely a failing on my part, not Molly Mae's! I decided to work on the tiling because I could see that the problem was very well crafted and I hoped that some left-brain people out there, who disliked the tiling part, would pick up the problem and carry it to a complete solution. Thanks, psykomakia, for the problem as well as your careful nurturing of it. (Am I confusing left-brained and right-brained? I don't really know).

I wrote a program to exhaust over all possible ways to tile the grid in the manner described in the puzzle.