[Guest]

The first puzzle i've posted... so here goes...

U have 12 mice, one of them being special. You also have an infinite supply of cakes. What is the minimum number of cakes u would use to identify the special mouse, given that-

Scenario 1: The special mouse eats slower than the rest of 'em

Scenario 2: the special one eats faster...

Scenario 3: it's not known whether the special mouse is faster or slower than the others

For all scenarios u do not have any knife or timer... just the mice and the cakes...

Have fun solving...

[plainglazed]

Nevermind the above. Rethinking. Cant see past my tail and my head's not helping either.

[Guest]

K guys another hint which i think wud definitely help...

U cud arrange the mice in a way such that the order the cakes finish in tells you which mouse is special.

-_-

[Guest]

K guys another hint which i think wud definitely help...

U cud arrange the mice in a way such that the order the cakes finish in tells you which mouse is special.

-_-

I was actually thinking about this alot but since we don't know how much faster or slower a special mouse eats I couldn't figure out a reliable method... For example a fast mouse could eat 10 times faster than a regular mouse. Or maybe a slow mouse eats practically nothing compared to a regular mouse.

I don't have time to return to the idea right now but I'll share what I started with to maybe help collectively come to a solution. Say you had 12 regular mice. put 6 on one cake, 3 on another, 2 on another and 1 on another. Once the 6 mice finish. Add 4 to the cake with 1 and 2 to the cake with 2. The remaining 3 cakes should finish at the same time this way. I hoped that by swapping the mice around once that first cake is finished and noting when they finished I could get somewhere. But I abandoned it because not knowing how fast or slow a special mouse is ruins it quite handily. And even if you assume a small difference for the special mouse, the 3 cakes only have 12 possible outcomes and there are 24 possible cases.

With 4 cakes there are 24 possible outcomes but not knowing the relative speed of a special mouse and having no way to time or estimate how much of a cake remains prevented me from thinking down those lines as well. But I'll pick it up again once I get to work tonight.

Edited May 7, 2010 by Tuckleton

[Guest]

So I've come up with a way to do it in 4. But I feel like it breaks the rules in 2 ways. First it assumes that there is a point during the consumption of a cake before it's all gone that you can be sure more than half of it is gone. You may not know exactly how much is left, but you know that at least half is gone (this may even be when there is only a tiny bit left). Practically speaking this isn't far fetched. Second, it assumes that the difference in speed of a special mouse is small compared to the speed of a regular mouse. (This isn't really that far fetched either since you'd need to have a fast mouse eating the cake of 4 mice to mess it up. But the bigger the discrepancy, the more accurate you need to be guessing the halfway mark). Anyways here goes:

4 cakes with 3 mice each. Once you can be sure that all of the cakes are past halfway done, take the 3 mice from each cake and split them up among the other 3 cakes. In this way there are still 3 per cake but they are all mixed up. Now the cakes will be finished following a pattern like this:

(a) A&B => C => D or

(b) A => B => C&D

If (a), then the mouse is slow and is the one you moved from D to C.

If (b), then the mouse is fast and is the one you moved from A to B.

Again, I have to say that I'm not too happy with this solution because of the rule bending...

Edited May 8, 2010 by Tuckleton

[Guest]

Sorry for double posting so frequently in this thread but I've got an improvement to my solution above.

Depending on how accurately you can measure when a cake is finished you could do the switch moments after starting instead of halfway. Then the solution is reversed:

(a) A&B => C => D or

(b) A => B => C&D

If (a), then the mouse is slow and is the one you moved from C to D.

If (b), then the mouse is fast and is the one you moved from B to A.

I feel this is much less of a breach of the rules since you don't have to estimate halfway and you'd have to have a mouse eating absurdly fast to make the relative eating rate matter.

Edited May 8, 2010 by Tuckleton

[bushindo]

Sorry for double posting so frequently in this thread but I've got an improvement to my solution above.

Depending on how accurately you can measure when a cake is finished you could do the switch moments after starting instead of halfway. Then the solution is reversed:

(a) A&B => C => D or

(b) A => B => C&D

If (a), then the mouse is slow and is the one you moved from C to D.

If (b), then the mouse is fast and is the one you moved from B to A.

I feel this is much less of a breach of the rules since you don't have to estimate halfway and you'd have to have a mouse eating absurdly fast to make the relative eating rate matter.

How about this approach. This approach makes a less restrictive assumption that, given four groups of mice started at the same time eating 1 cake each, we can at some point tell which group is eating slower or faster than the rest.

Here's the method, which requires 4 cakes

1) Divide the mice into 4 groups of three each.

2) Let each group eat 1 cake, and let all four groups start at the same time. At any time period, three groups will have b percentage of cake remaining, and one group will have c percentage remaining, where b is not equal to c.

3) As soon as we can tell which group is eating slower or faster than the other three groups (that is, as soon as we can tell if b > c or b < c ), withdraw the 4 remaining pieces, three of which will be the same size.

4) Feed these 3 pieces to the 3 mice in the special group.

Edited May 8, 2010 by bushindo

[Guest]

Sorry for double posting so frequently in this thread but I've got an improvement to my solution above.

Depending on how accurately you can measure when a cake is finished you could do the switch moments after starting instead of halfway. Then the solution is reversed:

(a) A&B => C => D or

(b) A => B => C&D

If (a), then the mouse is slow and is the one you moved from C to D.

If (b), then the mouse is fast and is the one you moved from B to A.

I feel this is much less of a breach of the rules since you don't have to estimate halfway and you'd have to have a mouse eating absurdly fast to make the relative eating rate matter.

Tuckleton ur answer is absolutely correct (after having reconfirmed with the guy who gave it to me....)

i understood the previous one was a little problematic if the special mouse was waaaaay toooo fast or waaaaay toooo slow....

amazing!!!!

[Guest]

How about this approach. This approach makes a less restrictive assumption that, given four groups of mice started at the same time eating 1 cake each, we can at some point tell which group is eating slower or faster than the rest.

Here's the method, which requires 4 cakes

1) Divide the mice into 4 groups of three each.

2) Let each group eat 1 cake, and let all four groups start at the same time. At any time period, three groups will have b percentage of cake remaining, and one group will have c percentage remaining, where b is not equal to c.

3) As soon as we can tell which group is eating slower or faster than the other three groups (that is, as soon as we can tell if b > c or b < c ), withdraw the 4 remaining pieces, three of which will be the same size.

4) Feed these 3 pieces to the 3 mice in the special group.

Again this solution wont work if the difference in the speeds of eating is very very small...

[Guest]

Thnx a lot everyone for contributing...

And tuckleton..u were the knight in the shining armor :lol:

i really want to know how much time u gave this puzzle per day....

ur solution was mind-blowing...

i guess i hav a long long way to go....

thnx a lot.

[Guest]

Solved.

[Guest]

Thnx a lot everyone for contributing...

And tuckleton..u were the knight in the shining armor :lol:

i really want to know how much time u gave this puzzle per day....

ur solution was mind-blowing...

i guess i hav a long long way to go....

thnx a lot.

Wow, thanks for the kind words. I have to admit I am my own worst enemy sometimes since I forced myself early on to stop thinking along the lines that turned out to be correct since I stubbornly labeled them as unfit methods given the constraints of the question as I saw it. Gotta try to remember to keep an open mind. As for how long I spent on the puzzle I only actually sat down to tackle it a few times apart from when writing my posts but it was definitely rolling around in my head all week!

Anyways, it was a very enjoyable puzzle and I hope to see more from you in the future!

Tuck

Edited May 11, 2010 by Tuckleton