It seems that I can never word this one brain teaser correctly but here it is in all its glory finally. It is number 4 from last time:
4. Correct version:You have 100 balls divided evenly into ten boxes (ten balls in each box). One of the boxes contains balls that are 1.5 grams lighter than the balls in the other boxes. You are given a digital weigh balance. How do you figure out which of the ten boxes contains the balls that are 1.5 grams less by using the balance only once– you can only take one digital reading. (Note: The boxes are numbered 1 through 10 and so are the balls from the boxes i.e. a ball from box 2 will be labeled 2)
1. Let us take a variation of the old problem with the 4 stones. Last time, you had four stones and one was either heavier or lighter. Now, you have eight stones and you know for sure that the odd one out is heavier. How do you find the heavier stone by using the weighing scale only twice? Remember this is the judge’s scale not the digital one.
2. A school has 1,000 students and 1,000 lockers, all in a row. They all start out closed. The first student walks down the line and opens each one. The second student closes the even numbered lockers. The third student approaches every third locker and changes its state. If it was open he closes it; if it was closed he opens it. The fourth student does the same to every fourth locker, and so on through 1,000 students. To illustrate, the tenth locker is opened by the first student, closed by the second, reopened by the fifth, and then closed by the tenth. All the other students pass by the tenth locker, so it winds up being closed. How many lockers are open?
3. The island of Elbonia have a rather eccentric postal system. Postage for an item can be anything from 1 dinari to 15 dinari, and you must use exact postage. Frustratingly, there is only space on the envelopes in Elbonia to attach a maximum of three stamps. What is more, they only have three different denominations of stamps, can you work out what they are?
4. What shape completes the bottom line?
triangle pentagon square
square hexagon hexagon square
pentagon hexagon hexagon hexagon square triangle
hexagon octagon octagon octagon octagon ==?==
Again, remember to leave your answers as comments. Hopefully, you get them all right!