Twenty metal blocks are of the same size and external appearance; some are
aluminum, and the rest are
duraluminum, which is heavier.
Using a pan balance to determine how many blocks are aluminum, what is the minimum number of weighings to be done?
So with only having to determine the number of each type, not having to label which is which, I believe I've found a method to do this with 11 weighings. This seems like a lot though...
Basically, the strategy is to produce a "standard wieght" contining 1 of each type of block, and then weight this against any remaining pairs of unknown blocks. Start by weighing one against another, ideally they are different and you've got your standard already. 9 more wighings against pairs of blocks will tell you how many of each there are. If the first pair are the same, weigh them against another pair - now youve got either 4 identical blocks or at least one different block (allows you to determine what the original two blocks were) and 10 more weighings will be required (you will be able to produce a "standard weight" by weighing the second pair against each other). If you are stuck with 4 identical blocks, weigh them against 4 more blocks and repaet as above, then again with 8 more blocks if still balanced. Finally, if the first 16 blocks are identical (which has taken 4 weighings, take a single block from this set and weigh against the final 4 to determine the total different weight blocks. All paths result in 11 or fewer weighings.
Now, I bet someone can top that...
hmm
