Last puzzle was lol haha... I think the best solution we can have is this one: Generate all nxn map possibilities. For each nxn map, create k different parrallel maps such that k is the number of empty points in the maze, imagine the robot at all of these positions. and attempt to give it U/D/L/R directions on all k maps. if the 1st did not solve, solve the current state on the second one, and do it on the third... ect.
ANYWAYS that was a bad one. Here's something more accessible.
You are a wine owner with 1000 barrels of wine, and they are going to be shipped by next day. However, one of the barrel is poisoned. You have 10 test tubes worth of testing chemicals that could test this poison in however minute amount, however, the testing takes a full day to yield result.
How do you do it?
Again, put answer in spoilers, collaborate if you don't have it, and have fun!!! :D
Technically there is no problem since you didn't say that there was a problem shipping poisoned barrels... But if that was a problem read this: + Show Spoiler +
You just take samples in such a way that you get the vials to be a binary basis. Like, the first vial you take from every other, the next vial you take from 2, then not from 2 etc, the next from 4 then not 4. Continue up with that till you get 512 which is the tenth vial. Now when the test comes you just transform back into the normal basis and voilà.
add 24 barrels of water 1 count them from 0 to 1023 just for fun 2 take samples from odd numbered barrels 3 remove the odd numbered barrels in order, and concatenate the strings of barrels so the line of barrels looks like 1,3,5,7...0,2,4,6... repeat from 1 until you have no more test tubes (count the tests as well, from 1 to 10) when test result are done, you take them from the 10th to the first: if positive write 1 on a piece of paper, else write 0 you can now "clear" half the barrels for human consumption so write OK on the barrels which are now obviously good(do i need to specify which or do you get it?) invert step 3 and do this until all test results are accounted for which will leave you with all but one barrel cleared also you can convert the number in base 10 if you don't do binaries and count that number backwards to the poisoned barrel hope i did not screw this up lol
there is like a general case for solving this kind of shit, like CD error correction but i don't really know a lot about this branch of math
Actually there is a very easy general method to solve this kind of problems: + Show Spoiler +
The problem will be solved if you can fill the vials with combined wine from the bottles in such a way so that there are no 2 different vials with wine from exactly the same combination of bottles and each bottle is represented in at least 1 vial (one bottle may not be represented because if all vials turn out to be clear then it is the poisoned one). It can be easily seen that in our case we can: For each bottle make a 10 digit binary number where we have 1 if the bottle is represented in the corresponding vial and 0 if not. So the problem is solved if we can generate 1000 different such numbers. But we can because all such numbers are 2^10 = 1024 > 1000.
On August 23 2009 20:06 MER wrote: Actually there is a very easy general method to solve this kind of problems: + Show Spoiler +
The problem will be solved if you can fill the vials with combined wine from the bottles in such a way so that there are no 2 different vials with wine from exactly the same combination of bottles and each bottle is represented in at least 1 vial (one bottle may not be represented because if all vials turn out to be clear then it is the poisoned one). It can be easily seen that in our case we can: For each bottle make a 10 digit binary number where we have 1 if the bottle is represented in the corresponding vial and 0 if not. So the problem is solved if we can generate 1000 different such numbers. But we can because all such numbers are 2^10 = 1024 > 1000.
EPT
