really hard puzzle, noone has solved yet...

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Since the XXX is derived from the 3 sets of given numbers and the ### is derived from these as well as the XXX, doesn't it follow that the ### is derived soley from the 3 sets of given numbers?

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not neccisarily.

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Then by "and the given numbers" you must mean more than the specific numbers that were used in the calculation of the corresponding XXX (i.e., some sort of progressive calculation in which numbers other than the corresponding numbers are used to calculate the ###). Otherwise, this doesn't seem to make any sense.

PS - Found some sort of calculation that worked for the 125 of RED125 and the 167 of CAT167, and was utterly heartbroken when it did not work for the 195 of ANT195.

I think I'll take a break.

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"74 76 68" are the only given numbers that are used to get the ###. that is all ill say for now.

what were the rules that worked for those 2 numbers? you might be on the right track.

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My rule, which as it turned out only worked for the first two number/letter combos, only works when you employ different rules for odd and even sums of the three preceding numbers.

Let x = even number
Let y = odd number

When sum(a,b,c) = x (where the sequence is "a b c LLL###"), then ### is calculated as follows:

### = 2x - (x/2 +1)

When sum (a,b,c) = y (where the sequence is "a b c LLL###"), then ### is calculated as follows:

### = 2y - ((y-1)/2)

Examples:

37 24 23 RED125
sum(37,24,23) = 84
84*2 - (84/2 + 1) = 125

30 49 32 CAT167
sum(30,49,32) = 111
111*2 - ((111-1)/2) = 167

So I got very excited until I was faced with 51 38 57 ANT195, which yielded the following result:

sum(51,38,57) = 146
146*2 - (146/2 + 1) = 218

The only thing I can safely say is that I'm fairly certain that the sum (or at least some linear combination of the preceding numbers) is involved in the formulation of ###. This must be the case because as the preceding numbers increase in magnitude as a group (i.e., the preceding numbers for RED < the preceding numbers for CAT < the preceding numbers for ANT, etc.) so do the ###s. This might be stating the obvious, but it rules out any other trivial use of these preceding numbers, such as summing all the digits within the numbers until you get a number less than 10, as this would not produce a direct correlation between the preceding numbers and the ###s.

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Was I close?

[billygrippo]

not really

[ddubois]

Can someone with mathlab or whatever solve for:
37x + 24y + 23z = 125
30x + 49y + 32z = 167
51x + 38y + 57z = 195
then see if the solution works for
56x + 44y + 57z = 231 and 76x + 68y + 73z = 287?

I tried to do it by hand, but when I got to "51 * ( 125/37 - 24/37 * (3465/1093 - 494/1093 * z) - 23/37 * z) + 38 * (3465/1093 - 494/1093 * z) + 57 * z = 195" I said [censored] this and quit.

[PokerPadawan]

That's what I was going to do, but I'm lazy. [img]/images/graemlins/grin.gif[/img]

[Bataglin]

Was my answer correct? I think it is. I posted it a couple of posts up, but can say it again (in white):

<font color="white"> OMG293 </font>

[billygrippo]

DING DING DING DING

CORRECT!!!!!!111


i missed your last reply.

[thedustbustr]

the linear algebra stuff doesn't work out.

[LotsOfOuts69]

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Was my answer correct? I think it is. I posted it a couple of posts up, but can say it again (in white):

<font color="white"> OMG293 </font>

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Ok its time for a solution explination.

Post it in white if you get a chance, thanks.

--LoO

[Bataglin]

No fancy math required, just good old fashioned addition and subtraction.

Hopefully I'll get it right from all my scrabbling... This is how I got it:

<font color="white">Each number in front of the word represent a letter. In the first case; 37 24 23 RED, the #37=R, 24=E and 23=D when A=20. For the next set, we get ATC when A=30. And so on: NAT when A=38, MAN when A=44, and WOT when A=54.

The "letter-value" increases with +10, +8, +6, +10. If we assume the next will be +8 again (A=62), we get the letters MOG.

The order of the letters goes like this: no change (RED), place the last letter first (CAT), then the second (ANT), no change (MAN), the last first (TWO), and the second letter first again (OMG).

The numbers were a struggle, but

Take the number following each word, and subtract the sum of the numbers making up that word. (125-84=41, 167-111=56, and so on). This gives us the row 41,56,49,74,70, in which the relations are +15, -7, +25, -4 (no pattern here to predict the next number).

Now back to the letters. Order the numbers making up each word in a manner so that the numbers is sorted in accordance with the word. 37 24 23 RED (remains the same), 32 30 49 will be CAT, 38 51 57 ANT, 56 44 57 MAN, 73 76 68 TWO, and 76 74 68 OMG. Now, subtract the second number from the first, and add the third; 37-24 +23=36, 32-30 +49=51 and so on. This gives us 36,51,44,69,65 and 70, and this string has the relation: +15, -7, +25, -4 and +5.Notice that this relation is the exact same we found before, but now we also have the next value; +5.

Returning to our original string, we can fill in the next:
41,56,49,74,70 and (+5) 75.

Now we simply add the sum of the numbers giving OMG (74+76+68)=218 with 75, and get 293. </font>

Now, one can't be 100% certain that the answer is correct in this kind of puzzles, there is always a possibility for some even deeper hidden solutions. And one can not be certain that the procedure mentioned is the same one the OP used, even when yielding the correct answer.

Admittedly, I would've found it very surprising if this answer wasn't correct, hence my joke-reply OMG WTF (in case it was wrong)

[LotsOfOuts69]

Nice Job, I got the letters the same way, but thought there must be some other way of doing it (i.e. I thought there had to be a reason it started at 30 (trying not to spoil))

Good job on the numbers.