Friday, December 4, 2009
Problem 6: How Many??????
A certain village in Jacobean times had all the valuables locked in a chest in a church. The chest has a number of locks on it, each with its own individual and distinct key. The aim of the village was to ensure that any three people in the village would amongst them have enough keys to open the chest, but no two people would be able to. How many locks are required and how many keys?
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Leo said...
ReplyDeleteDoes each lock only have 1 key.
Can a person have more than 1 key and is there a max amount of keys per person.
ReplyDeleteIt depends if each person can only have keys to one lock then the number of locks has to be 3. The number of keys is also three. One for each lock. Because for two people you would need one person to have two different keys which is not possible.
ReplyDeleteI might be wrong (Just made an inference.)
The way i take this problem is that there's more than one lock, and more than one key for each lock, and the church wants 3 people to hold all the keys. But this doesn't really make sense because it says there can only be one key per lock...... also there must be a lot of locks because people didnt want the responsibility of carrying so many keys..... It has to be a number that divides by three, as the church wanted 3 people to have the keys... my final answer is 12 locks
ReplyDeletebut there's multiple answers, if i interpreted the question properly!
ReplyDeletewhat if the town invested in a combination lock...??!!
ReplyDeleteOh wait it has to be a number divisible by 3 but not by 2 so it can not be 12 like Iris said. It could be; 3,9,15,21,27,33,39,45,51,57 etc.
ReplyDeletescratch what i said! it has to be divisible by 3 and not 2 as i said, but now i have to figure out how many locks, and what type they are.... I think i got an answer. I think that there would be a lock box with 3 locks on it. Three people would have to hold 1 key each! one normal pad lock key. So 1 lock box and 3 keys for that lock box. Other possibilities included:two lock boxes with 3 keys, 2lock boxes with 9 keys or maybe even one lock box with 3,9,15,21,27,33,39,45,51,57,63 etc
ReplyDeleteAlso there's a pattern the amount of locks that could be on the box go up by 6 each time!ie: 9-3=6 51-45=6 etc
-Iris
i hope i got it right this time :)
i believe that there is more then one answer. what i know of is that any multiple of 3, because as long as there is some number relation with 3 it is possible. fro eg. 3 people each have one key= to 3 locks. and each time it can increase by 3 or any other multiple of 3. in otherwords as long as it can divide by 3 it is a possible answer. i know that leo said that it shoul'd divide by 2, but 6 divided by 2 is 3 so i has a very large connection between the 2 numbers. i am very sure of my answers because i tried many types of possibility's by drawing them in a chart, and after concluding everything i had just done that is what my concluding statment was. as long as it can divide by 3 it is a correct answer to the lock key question.but i think 9 keys should be the max becuase carrying more then that would be very bothersome but sadly math is reality its just math.:(
ReplyDelete~Adele~
I said it should not be divisible by 2 because otherwise 2 people could open it.
ReplyDeleteI think the number of keys times the number of locks has to equal a number not divisible by 2 but divisible b 3. So 1 lock 3 keys, 3 locks with 6 keys each or 5 locks with three keys each.
ReplyDeleteleo is that your FINAL answer??!!
ReplyDeletelol
-Iris
roaaaaaar YOGI Is PISSED i just wrote and accidentally closed it stupid jelly bean forest RAAAAAAAAAAAAAAAAAAAAAAAAAAAAR anyways like i wrote b4 and u didnt SEEE it must be a multiple of 3 becuz three peeps have to open it even tho it could range from 3 to 300000 and it also depends on the amount of boxes and stuff but with a basic six lock sytem and one box it would be 6 keys and 3 ppl with 2 keys FROM: YOGI BEAR
ReplyDeleteHey everyone,
ReplyDeleteFirst I did 3 people in the village. I found that each person would have one different key and there would be 3 locks. So then I did 4 people and made a chart of all the 2 people combos that couldn't open the chest. I did that to because the number of combos would be the number of locks. So I found there would be 6 locks and 12 keys. Each person would have 3 keys.
Then I did the same thing for five people. There is 10 locks and 30 keys, 6 keys per person.
I did the same for six. There would be 15 locks and 60 keys (10 keys per person).
I'm going to make a table and try to figure out a pattern. I'll post another comment with the results.
*Katty*
HI!!!!!!!!The thingy has 3 locks right? so i used microsoft excel to make a table that was 6 GODDAMN PAGES!!! anyways, the number of locks is NOT NOR EVER WILL BE divisible by 2, but by 3. i got that by multiplyin the number of keys (in this case that be 3) by the number of locks. (which is also 3, i think) i was up until like midnight trying to figure this out but some how i got it. there probably is a pattern but that will take a college graduate to figure out. (or my dad who figured this out in like ten mins BUT WOULDN'T TELL ME!!) like adele, i think there is more than one answer. OR MAYBE ITS UNIVERSAL?!?!?!?! o.O
ReplyDelete-JoSeL
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-Josel-
there are more than one answer, as most people have alredy found out. 3 looks with 3,9,15,21,27,33,39,45,51,57,63 keys etc.
ReplyDeleteoops i mispelled "locks"
ReplyDeleteEPIC FAIL :(
-jeff
Hey,
ReplyDeleteIt's me, Katty, again. Ok so I did the table and found a pattern. So I found pattern rules for the number of people, locks, and keys. So the pattern for the number of people goes up by one each time (12345 etc). For the number of locks, each time you add a number, you add one to the previous number that you just added ( +3, +4, +5 etc). Ok then for the number of keys I got stuck because I couldn't find a pattern. So then I looked at the charts I made BEFORE for the combo of two people. Ok anyway, so I found that the number of keys is the number of keys per lock times the number of locks. Then I discovered (this surprised me) that the number of keys per lock is the number of people times 2. So if you extend the chart you can find the answers for numbers up to 50, 100. So that's how I got my answer (but there's probably different answers). Happy Holidays!!
*Katty*
P.S. Josel I don't think the math blog is used to post websites about talking cats. :P
I agree with Katty about the Josel thing... Especially because the're all the same....
ReplyDeleteLOL
And Josel, it wasn't Adele who said there are many answers... It was ME!
-Iris
The Oren Redinger Video thing is a mistake because he didn't sign out of his gmail and i didn't see it so that's what came up instead of Iris..... :(
ReplyDeleteIf each person has a key for each of the locks (so each person would have a key for locks A, B, C, D, E) then you have a second key hole on each lock (lock G). If each person took two G keys plus keys for each of the other locks then it would take at least three people to open the five locks. If only two people try to open the chest they could not open it because even though they have locks A-E they would still lack one G key. This works for 5 or more locks no matter how many people are in the village. There would be 7 keys per person if there were five locks.
ReplyDeleteLike IRIS said, I think there are a lot of possible answers, since the question does not give you enough definitive information. I'm not sure what kind of lock it is, so I'm going with this idea. Anyways, it was the only one I could think of. I think there are 3 locks, and the locks are of the same design. Each person gets one key. Ok, so how this works is that you need 3 people to open the 3 locks. This lock works such that you have to keep all the keys in the locks, and then turn the keys at the same time to open the chest. As well, everyone has only 1 key so they can't use another key to open the last lock. There are other ways to do it, but I think this is the simplest. I don't think it is 3 different keys because if you give out 3 different keys, then you are never sure who you will choose to open the locks. And if you give out 3 different keys, then 2 people can open the chest. (I might be wrong, and if I am, someone please tell me!)
ReplyDeleteHey,
ReplyDeleteOops sorry. I said before, the number of keys per lock is the number of people SUBTRACT two. Sorry I said times. Oops :)
Happy Holidays!!!!
C u 2morrow,
katty
P.S. Wow Iris you post a lot of comments! Lol!
OH WELL THOSE TALKING KATS ROCK >:)
ReplyDelete