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Peach's puzzle - two solutions?

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Buckeyeskickbuttocks

Buckeyeskickbuttocks

Z --> Z^2 + c
Staff member
OK, for those of you who have followed the Trivia thread, Peach posed the following puzzle:

[URL="http://www.buckeyeplanet.com/forum/attachment.php?attachmentid=2286&thumb=1&d=1131404745"]http://www.buckeyeplanet.com/forum/attachment.php?attachmentid=2286&thumb=1&d=1131404745[/URL]

(Numbers across the top: 5, 23, 9 and across the bottom: 20, 14, 20, 19, 24 Numbers in the middle of each triangle = 10, 2, ?)
Solve for "?"

Buckguy correctly determined that 20 = T, 5 = E and 14 = N in the first triangle and 20 = T, 23 = W and 15 = O in the second. From that he reasoned (Correctly) that 19 = S, 9=I and 24 = X so ? = SIX (6)

I, on the other hand, found the difference between the numbers at the poles of each triangle. Thus, on Triangle 1, 20 - 6 = 14, 20-14 = 6, 14- 5 = 9

On triange 2 - 23-20 = 3, 20-15 = 5, 23-15 = 8 and then

On triangle 3 - 19-9 = 10, 24-19 = 5, 24-9 = 15

Now, having drawn that out on paper I saw this easier. If you'd like to draw it, here's the rules: I labled each side of each triangle with the difference between the poles.

Thus, on T 1 the left side = 15 Bottom = 6 and Right = 9
T2 = RS = 3, B = 5, LS = 8
T3 = RD = 10, B = 5, RS = 13

Then, I noticed if you look at Triangle 1, taking the Right side (9) and add 1 you get 10 (the number in the midle of T1) Proceeding to T2, I noticed if you take the next side (counterclockwise) - that is the Left side - you see a 3. 3 - 1 = 2 and 2 is the number in the middle of the triangle.

So our pattern is RS + 1 = Answer on T1; LS - 1 = Answer on T2.

Then, I noticed the Bottom of T3 (conforming to the idea of moving counter clockwise) had a 5. 5+1 = 6 Thus "?" = 6

So, Buckguy PM's me and we discuss the following: If we take the other three letter number, ONE, my code will break down whereas his will not and thus his answer is right. I don't disagree. However, I note: Maybe so, however, we were not given the 4th triangle, thus without that information, my cracking of the code stands up, and with little effort I could construct a new triangle that conforms to my code cracking rules. In that we don't know what triangle 4 is, either one of us may be right.

Then, it also occurred to me, even had we a 4th triangle, we could both be right. Here's how.

Everything is the same in terms of how we solve the problems. What's important is the 4th triangle's answer is 1.

Now, if I'm writing some sort of coded encrytpion, I may well put a "key" in the puzzle, so that a person can crack the code. Lets assume I WANT the code cracked for some reason. Anyway, it makes sense to me to encode the "Key" differently than the other numbers. The other numbers (that is, 10, 2 and 6) follow the rules I identified, where as the last triangle, T4 follows no such rule. It's answer is 1. ONE, is the number I used, adding or subtracting in succession, to break the code of the other triangles. Thus, T4 could not conform to the rules for the rest of the puzzle, and still be nothing more than a Key so as to crack the puzzle.

My solution would allow for a 5th triangle (as well as any number of triangles) all following the same "key - code" sequence of T1 - T3), whereas Buckguy's solution does not. Regardless, Peach's puzzle has 2 solutions, and the "real" solution can never be determined with 100% accuracy UNLESS there are a minimum of 5 Triangles. In that case, we know that it must be a code such as I've outlined - and then we have to detemine what the numbers, 10, 2, 6 and maybe 1, might mean. they may well be letters, and thus I can write a sentece using this triangle system. Since there are no more three letter numbers, we can never have more than 4 triangles if Buckguy's answer is correct. But, as explained above, we still can't say for sure based on only 4 Triangles whether my explaination or his is what was intended. Both are correct.

Make sense?
 
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On triangle one, you subtracted 6 from 20, but the other corner is a 5.

Does that ruin your solution? I'll let you work it out. :wink2:
 
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Not only did I read that, I read it twice more to make sure I was following. I think that both answers would be correct, but that Buckguy Bin Laden's answer was the answer for which the creator of the puzzle was looking. :nerd:
 
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Is this a problem?

24-9 = 13

edit - I followed your logic, and this doesn't matter either.

But I also think your solution is too much of a stretch to identify a pattern, and that it should not be called a solution to the puzzle.
 
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Hmmm.... That seems a little convoluted, BKB. I see your point, but it seems to me like you're trying to force a square peg into a round hole to make this work. BB pointed out one flaw already, though from the rest of your solution, subtracting 6 from 20 rather than 5 doesn't really matter, since you aren't using that side of triangle 1 anyway. Your solution actually makes many of the numbers in the puzzle completely arbitrary and pointless. By your reasoning, I could put any random number in the bottom left corner of the first triangle, since 14-5 = 9 is the only side you used. Same, of course, goes for the bottom right corner of triangle 2 and the top corner of triangle 3.

Also, the introduction of a fourth or fifth triangle seems suspect to me. My reasoning on such matters is that you may use only the information on the page, and that you should use all of the information on the page.

I'll have to give this some more thought later, as I am a little busy today, but my inclination is to apply Occam's razor here. You seem to be making too many assupmtions. Usually, the simplest, most elegant solution is the correct one. And, of course, since Buckguy's solution is the solution I intended, it must be right! :)
 
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PrincessPeach said:
Hmmm.... That seems a little convoluted, BKB. I see your point, but it seems to me like you're trying to force a square peg into a round hole to make this work. BB pointed out one flaw already, though from the rest of your solution, subtracting 6 from 20 rather than 5 doesn't really matter, since you aren't using that side of triangle 1 anyway. Your solution actually makes many of the numbers in the puzzle completely arbitrary and pointless. By your reasoning, I could put any random number in the bottom left corner of the first triangle, since 14-5 = 9 is the only side you used. Same, of course, goes for the bottom right corner of triangle 2 and the top corner of triangle 3.

Also, the introduction of a fourth or fifth triangle seems suspect to me. My reasoning on such matters is that you may use only the information on the page, and that you should use all of the information on the page.

I'll have to give this some more thought later, as I am a little busy today, but my inclination is to apply Occam's razor here. You seem to be making too many assupmtions. Usually, the simplest, most elegant solution is the correct one. And, of course, since Buckguy's solution is the solution I intended, it must be right! :)
Click to expand...

I agree, Peach. He was trying to read too much 'Inuit'. :wink2:
 
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