- #701
Ibix
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He climbed on a block of ice to tie the rope. It subsequently melted, leaving a water stain and a locked room mystery.
This is correct. (It is the solution to the hanging man enigma.)Ibix said:He climbed on a block of ice to tie the rope. It subsequently melted, leaving a water stain and a locked room mystery.
Yes. I like your solution in that it's far easier to conceptualize compared to mine, me thinks.Ibix said:Regarding the dalmations, I think collinsmark's solution is correct, but can be expressed rather more simply.
It is indeed a proof by contradiction. Imagine a set of eleven dogs from which we cannot pick a subset divisble by eleven. Line the dogs up in a row - sit! Stay! Let us say that the ith dog has Si spots.
In front of each dog, write the remainder when its spots plus the spots of all dogs to its left are divided by eleven. That is, in front of the ith dog, write the remainder when [itex]\sum_{k=1}^i S_k[/itex] is divided by 11.
You now have eleven numbers. If any two of them are the same, then the intervening dogs' spots must add to a multiple of 11 (so if the nth and mth remainders are the same then [itex]\sum_{k=n+1}^m S_k[/itex] is divisible by eleven.
So if no sets are divisible by eleven then you have eleven distinct non-zero remainders from division by eleven - but there are only ten such numbers. That is a contradiction - therefore you can always find a subset whose spots add to a multiple of eleven.
Is it something as simple as saying "I will shoot the first one to come out", after which they will all wait for another one to go first?
Office_Shredder said:consciousness, if the guard does that then as a prisoner I
shove another prisoner, making him stumble and wasting the guard's bullet
Enigman said:Or everyone agrees to go together...
1/n chance...
So? The other prisoners still escape. The act of moving first is random and hence all of them as far they are concerned have 1 -1/n chance of survival.consciousness said:It is assumed that the guard is very alert. He can detect this small lag and know who moved first. (In hindsight a programmable turret gun would have worked better)
Enigman said:So? The other prisoners still escape. The act of moving first is random and hence all of them as far they are concerned have 1 -1/n chance of survival.
Office_Shredder said:Assuming it takes the prisoners more than one second to escape the guard's line of fire: Assign the prisoners numbers 1,...,n. Then the guard announces "When the shield goes back up I will kill the prisoner whose number is lowest that is not inside the shield.
1 can't try to escape or he will die. 2 knows this, so knows he can't try to escape either. Etc.
Enigman said:Next one-
cArma said:Samuel Morse. No need to search. Answer is in the URL of the picture.
Office_Shredder said:Assuming it takes the prisoners more than one second to escape the guard's line of fire: Assign the prisoners numbers 1,...,n. Then the guard announces "When the shield goes back up I will kill the prisoner whose number is lowest that is not inside the shield.
1 can't try to escape or he will die. 2 knows this, so knows he can't try to escape either. Etc.
consciousness said:Wow I can see you!
There is a subtle difference.CompuChip said:Is this fundamentally different from what I said initially?
Enigman said:Next one-
.-- --- .-- / -.-- --- ..- / -.-. .- -. / ... . . / -- .
Google search is allowed.
Enigman said:It was foretold by The Oracle of Delphi that Homer would die in the island of Ios and that he should beware of a riddle posed to him by some young boys. Well obviously old Homer disregarded the prophecy and while he was walking on the banks of Ios a group of fisher boys asked him a riddle:
“What we caught, we threw away; what we didn’t catch, we kept. What did we keep?”
Unable to solve the riddle, Homer eventually died on the island, refusing to leave until he discovered the answer. So can you solve it?
(Googling is not allowed)
collinsmark said:Is it bait?
Enigman said:
“What we caught, we threw away; what we didn’t catch, we kept. What did we keep?”
Hmmm...*Scratches the E head* might work but not the answer the fishermen were talking aboutcollinsmark said:Hmm. How's about this guess:
"Mistakes." As in, if you catch your mistake in time, you can conceivably correct it (the mistake goes away), and all is good. But if you don't catch your mistake in time, you have to live with it.
Enigman said:It itches...