The family of giants you work for is throwing a fancy dinner party, but there’s a problem — the elder giant’s favorite shirt is wrinkled! To fix it, you’ll need to power up the giant iron. It needs two batteries to work, but the baby giant mixed the working battery pile with the dead pile. Can you test the batteries so that you get a working pair in seven tries or less? Alex Gendler shows how.
The family of giants you work for is throwing a fancy dinner party, and they all want to look their best. But there’s a problem – the elder giant’s favorite shirt is wrinkled! To fix it, you’ll need to power up… the Giant Iron.
The iron needs two giant batteries to work. You just had four working ones and four dead ones in separate piles, but it looks like the baby giant mixed them all up. You need to get the ironworking and press the giant shirt fast – or you’ll end up being the main course tonight!
How can you test the batteries so that you’re guaranteed to get a working pair in 7 tries or less?
You could, of course, take all eight batteries and begin testing the 28 possible combinations. You might get lucky within the first few tries. But if you don’t, moving the giant batteries that many times will take way too long. You can’t rely on luck – you need to assume the worst possibility and plan accordingly.
However, you don’t need to test every possible combination. Remember – there are four good batteries in total, meaning that any pile of six you choose will have at least two good batteries in it. That doesn’t help you right away since testing all six batteries could still take as many as 15 tries. But it does give you a clue to the solution – dividing the batteries into smaller subsets narrows down the possible results.
So instead of six batteries, let’s take any three. This group has a total of three possible combinations. Since both batteries have to be working for the iron to power up, a single failure can’t tell you whether both batteries are dead or just one. But if all three combinations fail, then you’ll know this group has either one good battery or none at all. Now you can set those three aside and repeat the process for another three batteries. You might get a match, but if every combination fails again, you’ll know this set can have no more than one good battery. That would leave only two batteries untried. Since there are four good batteries in total and you’ve only accounted for two so far, both of these remaining ones must be good.
Dividing the batteries into sets of 3, 3, and 2 is guaranteed to get a working result in 7 tries or less, no matter what order you test the piles in.
The iron comes to life with no time to spare, and you manage to get the shirt flawlessly ironed. The pleased elder and his family show up to the party dressed to the nines … well, almost.