Liverpool FC Forum

[112-1077774096]

when they all get together in the courtyard they just ask each other if they have all been in the room or not, if some say they havent been in then thats the answer, if they all say they have been in then thats the answer

[dawson99]

when they all get together in the courtyard they just ask each other if they have all been in the room or not, if some say they havent been in then thats the answer, if they all say they have been in then thats the answer

no, the point is that they have to meet in the courtyard before they start going in the room.

[account deleted by request]

xy - y = x5 - y4 - y3 = 20; x>0, y>0.  thats my mathematical solution anyway
The prisoners should decide that whoever is the first prisoner to enter the room after their huddle is the leader (as  'elected' by the guards).
He turns on the light, and is the only person allowed to turn on the light.
Each and every other prisoner turns off the light if and only if the light is already on and if they have not already done so.
When the leader turns on the light for the 100th time (this includes the first one), time to be free! Of course, as the leader has to return to the room 100 times, it could take over 27 years...

the only problem with my solution is it would take 27 years

This one works, but 27 years ?

[112-1077774096]

when they all get together in the courtyard they just ask each other if they have all been in the room or not, if some say they havent been in then thats the answer, if they all say they have been in then thats the answer

no, the point is that they have to meet in the courtyard before they start going in the room.

so they agree that only if they go in twice will they toggle the light, on the last day when the last prisoner goes in, if the light has been toggled he knows someone has been in twice so that means someone has had to miss out

[dawson99]

Actually, this riddle was sent to me by soeone i know at berkely in usa, and they have never solved it either... heres some more tips to help...maybe

Note 1: (1/8/2003 3:51PM Update) What is meant by optimal? If your solution is optimal, it means you can prove that no other algorithm can produce a lower average running time. This is usually very hard to do though, and I would be surprised if anyone ever sends me such a proof. So the best we can do in the meantime is try to beat the best average running time we know of. The number to beat so far is around 3500 days. So BEFORE YOU E-MAIL ME YOUR SOLUTION, check its average time to see if beats the 4000 day ballpark. If you get a number around 27-28 years, then you've found the solution most people who solve the puzzle come up with. However, it's not optimal.

Note 2: (1/8/2003 3:49PM Update) How to compute average running time? The preferred method is to do a probabilistic analysis using pencil and paper. But if you haven't learned about stuff like that, a much simpler way is to just program your solution and run it maybe 100 times, recording how many days elapsed in each invocation. Afterwards you should have an array of 100 numbers. Now take the average of all them, and you'll have an empirical average which is close to the theoretical one.

Note 3: (11/7/2002 7:35AM Update) The problem statement used to say "The prisoners are allowed to get together one night to discuss a plan." In the forum, quite a few people mentioned the clever solution of simply having the planning meeting in the central living room, and then asserting that everyone has been there on the first day of the random selection process. To assure that this problem is not so easily defeated, I have stipulated that the meeting happen in the courtyard.

[account deleted by request]

I think we should stick to Stmichael and his 7 + 5 are 13 type riddles mate

[stmichael]

Today's batch is a maths lesson:


A teacher says: I'm thinking of two natural numbers bigger than 1. Try to guess what they are.
The first student knows their product and the other one knows their sum.
First: I do not know the sum.
Second: I knew that. The sum is less than 14.
First: I knew that. However, now I know the numbers.
Second: And so do I.
What were the numbers?


The day before yesterday I was 25 and the next year I will be 28. (This is true only one day in a year.) When was I born?


What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?


Can you use all 9 numerals - 1, 2, 3, 4, 5, 6, 7, 8 a 9 - above and below a fraction symbol in a random order, to create a fraction equalling 1/3 (one third)?


What 5-digit number has the following features? If we put numeral 1 at the beginning, we get a number three times smaller, than if we gave the numeral 1 behind this number.


In the following "equation" 101 - 102 = 1 move one numeral, in order to rectify it.

[dawson99]

i could answer these, but as a bookies i know all the answers:blues:

[account deleted by request]

no 2  feb 28 th Wrong      



Well done Dward 

[account deleted by request]

Wheres Dward when you need him ?

[account deleted by request]

no 6=  101-10 squared (I dont know how to show a little 2)

[dward]

Wheres Dward when you need him ?

Here I am!

Today's batch is a maths lesson:


A teacher says: I'm thinking of two natural numbers bigger than 1. Try to guess what they are.
The first student knows their product and the other one knows their sum.
First: I do not know the sum.
Second: I knew that. The sum is less than 14.
First: I knew that. However, now I know the numbers.
Second: And so do I.
What were the numbers?


The day before yesterday I was 25 and the next year I will be 28. (This is true only one day in a year.) When was I born?


What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?


Can you use all 9 numerals - 1, 2, 3, 4, 5, 6, 7, 8 a 9 - above and below a fraction symbol in a random order, to create a fraction equalling 1/3 (one third)?


What 5-digit number has the following features? If we put numeral 1 at the beginning, we get a number three times smaller, than if we gave the numeral 1 behind this number.


In the following "equation" 101 - 102 = 1 move one numeral, in order to rectify it.

1) I don't know - for now.

2) He was born on December 31st and said it on January 1st.

3) 5.9

4) 5832/17496 - that took ages to find out.

5) I don't know.

6) Move the number 2 half a line up so you get 101-102(squared)=1.

No more maths please st.mike!!!

[account deleted by request]

NO 1             =            2 AND 9

[account deleted by request]

NO 5 = 42857.

[JC_81]

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