superprismatic

Got me! Good work.

Xamdam, I actually decoded two things but I don't see how one was a hint for the other. I used both to form my response, though. Please explain the "hint" portion eventually -- I'm curious.

No, I didn't see any hint code. I just went straight for the jugular!

Here goes: ....../..=...

OK, but they don't cycle. The last two digits of the last number (in this case Fibonacci) must be the first two digits of the first number (in this case Square). I'm afraid you don't have any solutions to the OP here.

Actually, I was just fishing to see if mySQL could handle much bigger things here than single digits. I know absolutely nothing about mySQL so I can't criticize. But I'd like to get some idea of how big a problem it can handle. I'd like to see allowing ABCDEF to be in the range 0-100 or 0-1000 or 0-10000, etc. and seeing how that affects the runtime. Thanks.

Well, what if you wanted the variables to go up to 1,000,000 instead of 9? How would that change your script? And what would its output look like?

I didn't see any Fibonacci number in there nor did I spot a cycle. Please elaborate.

I just caught my mistake. In my previous post, I used the number of distinct arithmetic progression triples instead of the number of Ns. Some Ns have more than one progression associated with them. So,

A very interesting choice of units indeed. It's useful to know when you're discussing gravity with a horseman in the British commonwealth!

What's the value of the acceleration of gravity at sea level on earth in furlongs per square fortnight?

Well, mmiguel1 gave several proofs of his contention that 5 is the answer. They were clear and concise. I can't imagine anyone arguing with his very nice explanations. Even if the proposer of the problem gives a different answer, I wouldn't believe it. Nice explanations you gave there, mmiguel1!

Good going! I don't know how small the number of letters can get, but I can't wait to see the smallest you puzzlers can come up with!

I can fit the surnames of all 38 presidential surnames into an 18 by 12 grid as follows: MSEYAHM-GNIDRAHSUB NOXINJC--GNANAHCUB RRN--EKNAGAERADAMS UEORFFILLMORETNARG HTTOOFNOSLIWF-A-NH TRGORELYTSEGDILOOC RANSDREWOHNESIEOSL ACIE-SYNERUBNAVLII MKHVNOSKCAJC-EE-DN ALSE-NOSNHOJROLYAT BOAL-TAFTLPIERCEMO OPWT-KENNEDYTRUMAN [/code] Every letter in this grid is part of at least one presidential surname. These names are written in the grid either vertically, horizontally, or diagonally. They may also be put in forwards or backwards. Usually, leftover grid positions, here containing a dash, are replaced by random letters. This, then, becomes a word search puzzle. The solver is asked to find all the target words (in this case, presidential surnames) which are in the grid. The tables could be turned and we can make a much harder puzzle: Find and fill the smallest possible rectangular grid (in terms of the number of cells) which contains all presidential surnames in word search puzzle fashion. But I propose the following puzzle: Place all presidential surnames in word search fashion in such a way that the partially filled-in grid made this way contains the fewest letters. For example, this grid contains 189 letters and all required surnames: [code] ----------------C-V------------- ---------------L--A------------- --------------E---N------------- -------------VI---B----------R-- ------TFAT--E-SEN-U---------E--- ---------MTLEVESOOR--R-----T---- ECREIPML--AG--NOSREFFEJNH-R----- --L---AI-NDBUCHANAN--L-ADAMS---- ---I--DNDI--O-OOH-AO-YRMC-Y----- ----N-ICLY--H-WFO-G-MT-U-K-E---Y -----TSOE-N-RAEOJVA-H--R--S-S-D- ------OLI-NOSIRRAHEUG--T---O-E-- -----CNNF-LHSUBDO-RR-----P--N--- -----I--RYI--L--IMA------O-N---- ----K---AN---NIXONL------LE----- ---C---TG------WT-GL-----K------ --M----T------------I----------- ------O--------------F---------- -----N-------------------------- Can you find a grid which contains much fewer than 189 letters? Here is the complete list of presidential surnames (comprising 252 letters): EISENHOWER WASHINGTON JEFFERSON CLEVELAND ROOSEVELT VANBUREN HARRISON FILLMORE BUCHANAN GARFIELD MCKINLEY COOLIDGE MADISON JACKSON LINCOLN JOHNSON HARDING KENNEDY CLINTON MONROE TAYLOR PIERCE ARTHUR WILSON HOOVER TRUMAN CARTER REAGAN TYLER ADAMS GRANT HAYES NIXON OBAMA POLK TAFT FORD BUSH [/code]