20051021, 22:38  #1 
Aug 2005
Brazil
2·181 Posts 
Some puzzles
I thought the puzzles forum was a bit cold, so...
1A company called a meeting such that the probability of at least two members having a birthday on the same date is higher than 50%. What is the minimal number of members possible present? 2What is the number hidden? (Don't multiply, please.) 847398654*638952=54144706?770608 3Two smart students (X and Y) choose a number and show it to their teacher. The teacher says that the result of the addition of both is either 1994 or 2990. He asks X, do you know Y's number? No. He asks Y, do you know X's number? No. He gives time to think about it, and in the next day... He asks X, do you know Y's number? No. He asks Y, do you know X's number? Yes, I do! What is X's number? (And Y's?) I didn't solve 4 and 5... 4For what positive integers m and n is it possible to build an melement set of positive integers such that the sum of any n of them is not divisible by n? 5A tweak of the Monty Hall: A show host shows to a guest n closed doors.(n is an integer, greater or equal to 3) Behind one of the doors is a car, the other ones, a goat. The guest picks a door. After that, the show host opens a door (with no car behind it). The guest, then, has to switch to a door not open yet, and so it goes, until there are only two doors (one chosen and one closed). The guest has to switch and sees if he's won the car or not. a)What's the chance that the guest wins the car? Try to be as objective and simple as possible (with the least number of operations) b)What's the chance when n tends to infinity? You can use only addition, subtraction, multiplication, division, and the number e. 6 You have a round table, and an infinite number of coins. You play a game with your friend, where you must place coins on the table (no overlaps). Who plays last wins. Would you like to start? Why? (Strategy) Good luck 
20051022, 12:33  #2 
Feb 2003
76_{16} Posts 
For n°3, IF x and y are integer and > 0
x+y = 1994 or x+y = 2990 x says no => x < 1994 y says no => y < 1994; y>996 x says no => x < 998; x>996 => x = 997 y = 997 Last fiddled with by flava on 20051022 at 12:33 
20051022, 13:32  #3 
Aug 2005
Brazil
101101010_{2} Posts 
7 A superstitious girl, when she was numbering her 200 page diary, started from number 1 but jumped every page where the numbers 1 and 3 appeared together, in any order. What was the number she wrote on the last page?

20051022, 15:27  #4 
Jan 2005
Caught in a sieve
612_{8} Posts 
1two :razz:
It's a trick question. If the company calls a meeting of two people who they know have the same birthday, the probability that they have the same birthday is 100%! 
20051022, 21:53  #5 
Jan 2005
Caught in a sieve
2·197 Posts 
5a: It depends what point in the show you're at.
If you're at the beginning (case a), the chance of winning is: n1 in n Not choosing a door at the end is equivalent to our guest choosing at the beginning, "I won't try door number m", for some m<=n. Then he tries all the other doors, in any sequence. If the car is behind a door other than m, he wins. So the chance the car was behind m and he loses is 1 in n, so his chance of winning is n1 in n. On the other hand, if the contestant is down to two doors when we start this scenario, (case b), his chances are always 1 in 2. 5b: In (case a), lim(n>inf)(n1)/n = 1 In (case b), lim(n>inf)1/2 = 1/2 7: The command "jot  1 1000 1  grep v "1.*3\3.*1"  head 200" produces all the page numbers. They start at 1, and end at 222. 
20051023, 00:20  #6  
Aug 2005
Brazil
552_{8} Posts 
Quote:
Quote:
Sorry? I can't get this number. I got 213 and my teacher keeps saying that the answer is 214!!! Can you list all the "jumped" numbers? Quote:
Maybe if the host opens m... Last fiddled with by fetofs on 20051023 at 00:20 Reason: Couldn't spoilerize :( 

20051023, 00:46  #7 
May 2003
1547_{10} Posts 
Problem 6: Yes, you want to go first. You put your first coin in the middle. Then, whatever your opponent does, you go diametrically opposed to them.
If they can move, so can you. So you will play last. Note that this solution doesn't require the table to be round. Only that it have a line of symmetry. Last fiddled with by ZetaFlux on 20051023 at 00:47 
20051023, 02:17  #8  
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Quote:


20051023, 04:51  #9  
Jan 2005
Caught in a sieve
2·197 Posts 
Quote:
13 31 103 113 123 130 131 132 133 134 135 136 137 138 139 143 153 163 173 183 193 213 Did you mean appeared together contiguously? Then I get 214. It can't be 213 because that's 213! P.S. This came from your teacher? Quote:
Last fiddled with by Ken_g6 on 20051023 at 04:53 

20051023, 12:18  #10 
"Mark"
Apr 2003
Between here and the
1794_{16} Posts 
Regarding the Monty Hall problem, in the original problem you have 3 doors and he will always open a door with a goat. By switching you have a 2/3 chance of winning (since your original choice was 1/3). In this version you are forced to switch after that door is opened, giving you a 2/3 chance of winning.
As the number of doors increase, I believe that the probability remains at 2/3 because you are forced to switch after each door is opened, which is unlike the original Monty Hall problem where n2 doors are opened and you then have the option of switching giving you a (n1)/n chance to win if you switch. 
20051023, 17:56  #11  
Aug 2005
Brazil
2·181 Posts 
Quote:
8Prove that any square isn't a perfect number. P.S: Oh, these guys are tricky!!!! I never thought about 213 

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