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Topic: Enigma Number 1606 (Read 1782 times) |
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TenaliRaman
Uberpuzzler
I am no special. I am only passionately curious.
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Re: Enigma Number 1606
« Reply #1 on: Sep 14th, 2010, 10:44am » |
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As it stands, I am not sure enough information is available. I am getting at least two answers. And if one of those is the expected answers, that lock can be broken by simply trial and error (without resorting to any math).
So yeah, I am finding the question ambiguous.
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grad
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Re: Enigma Number 1606
« Reply #2 on: Sep 14th, 2010, 5:34pm » |
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So, can you tell me how you get those two answers?
Did you use a program or what?
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towr
wu::riddles Moderator
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Re: Enigma Number 1606
« Reply #4 on: Sep 15th, 2010, 1:40am » |
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Bart Schipperijn's explanation of the problem in the comments seems to be the right approach.
The weight of the balls is one of 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721
The weights next to the scale have a weight from 4000, 2000, 1000, 800, 500, 400, 250, 200, 160, 125, 100, 80, 50, 40, 32, 25, 20, 16, 10, 8, 5, 4, 2, 1
There's just one value for the weight that singles out one total weight for the balls.
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| « Last Edit: Sep 15th, 2010, 1:40am by towr » |
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towr
wu::riddles Moderator
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Re: Enigma Number 1606
« Reply #6 on: Sep 17th, 2010, 2:13am » |
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For 1602
21-29 are superfluous, because if one of them were wrong, then either one of 1-9 or 20 would be wrong as well. So given that only one is wrong, it's in 10-19.
It's easily deduced that T+E+E+N=10, so we can scrap 14,16,17,19. Because if one of them were wrong, 4,6,7 or 9 would also be wrong. That leaves just 10,11,12,13,15,18.
If we assume T+E+N =/= 10, then we run into a problem, because we have F+I+F=5 implying I is odd, but T+H+R+E+E=T+H+I+R implies I is even, so therefore T+E+N=10=T+E+E+N ===> E=0.
Equation 13 then implies 9 is even, so 13 has to be wrong.
Then, from eight and eighteen we can deduce N=10;
N+I+N+E=9 ===> I = -11
T+H+I+R+T+E+E+N = 3 + 10 + -11 = 2
E=T=0
N=10
F=V=8
I=S=-11
O=-9
W=11
Y=-1
L=-7
X=28
H+R=3
U+R=5
G+H=19
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| « Last Edit: Sep 17th, 2010, 2:43am by towr » |
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Immanuel_Bonfils
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Re: Enigma Number 1606
« Reply #7 on: Sep 17th, 2010, 6:13am » |
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Sure! Didn't notice that 18 is also an exception in the "teen"s ...
edit: hide
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| « Last Edit: Sep 17th, 2010, 6:15am by Immanuel_Bonfils » |
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Immanuel_Bonfils
Junior Member
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Re: Enigma Number 1606
« Reply #8 on: Sep 17th, 2010, 6:32am » |
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Think would be easier to get E = 0 from 14, 16, 17,19 minus 10.
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towr
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Re: Enigma Number 1606
« Reply #9 on: Sep 17th, 2010, 6:44am » |
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on Sep 17th, 2010, 6:32am, Immanuel_Bonfils wrote:| Think would be easier to get E = 0 from 14, 16, 17,19 minus 10. |
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You can't from the outset assume 10 is correct. 4/14, 6/16, 7/17, 9/19 tells you T+E+E+N=10, but if T+E+N isn't 10, then E isn't 0 either. So you have to prove that E=/=0 leads to a contradiction.
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| « Last Edit: Sep 17th, 2010, 6:48am by towr » |
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