HBH Logical 1: Bags and Beads
The first of Hellbound Hackers’ logical challenges is Bags and Beads:
You are given 5 bags. There are 10 beads in each of the bags. In four of the bags, the beads each weigh 10 grams. In the remaining bag, each bead weighs only 9 grams. All the bags and beads look and feal identical. You must find out which bag has the lighter beads. You can use a scale, but it has to be a single-tray scale, not a two-tray balance scale. Also, you may use the scale only once. After you place something on the scale it will get stuck so taking anything off or putting anything on will not be weighed. You cant tell the difference by picking them up, they will all feal the same. How can you find out which bag has the lighter beads?
This challenge requires thinking outside of the box, which makes it a good exercise for hackers. You must realize that you are not limited to weighing the bags that already exist.
Take one bead from the first bag, two beads from the second bag, three beads from the third bag, and four beads from the fourth bag. You can leave the fifth bag. Put all the beads you picked up on the single-tray scale, and see what their total weight is.
If they weigh 100 grams, all of the beads are 10 gram beads, and therefore the fifth bag must contain the lighter beads. If they weigh 99 grams, 1 bead is lighter. Then the first bag must contain the lighter beads, since you picked one bead from that bag. With the same logic, it’s the second bag if the beads weigh 98 grams, the third if they weigh 97 grams, and the fourth if they weigh 96 grams.
Note that this solution is easier than some other solutions, since they state that you need five beads from the fifth bag. You don’t, though: and it’s easier to weigh 10 beads than 15.
Använder FireStats