A young lady got lost in a museum. There is a 80% chance that she is in the dinosaur section, and a 20% chance that she is in the aquarium section. Six people are available to search for her. Each searcher has a 20% chance of finding her. If you can only do one search, [...]
This was said to be a complex estimation of how much water will seep out of a reservoir. One thing you should understand is the top surface area is given, but the seepage comes from the surface of the ground under the water. For a specific reservoir, a table can help you estimate [...]
Alice and Bob play the following card game. Each has a shuffled deck of cards. Each takes the top card from their deck. If they match, Alice wins. If they don’t match they take the next card from the top of the deck. They continue like this until either they draw a matching pair, and [...]
You have a box with n shoelaces in it. You randomly pick two ends and tie them together. You then repeat this process until there are no free ends left.
On average, how many loops will you have created?
How many laces are needed to get (just over) 2 loops on average?
This is a non-trivial extension to the previous blockbuster problem.
Use b blue, 3 green and 3 red blocks, to form a ring. If no reds are allowed to touch each other, and no greens are allowed allowed to touch each other, how many unique patterns can you form?
To keep things simple, rotated versions of a [...]
Under what circumstances is/isn’t C(n,r) divisible by n?
Assume that n and are r integers (include 0 and negatives).
C(n,r) = n! / ((n-r)! r!)
You might find it convenient to use e.g. a|b for “a divides b”
and a¦b for “a doesn’t divide b”
On my British keyboard, the | is next to the Z and
the ¦ is next [...]
Here’s a repost from many years ago. I have no idea how to do it or what the answer is.
A boy has four red blocks and eight blue blocks. He arranges the twelve blocks uniformly randomly, in a ring.
What is the probability that no two red blocks are next to each other?
As I strongly suspect [...]
A block of ice measuring 1 foot by 1 foot at the base is placed in a 2 foot by 3 foot aquarium. Water is then added to a level of 9 inches. Once the ice melts, the level of the water remains at 9 inches. How tall was the block of ice?
A 2 foot by 3 foot aquarium is filled with 9 inches of water. A 1 foot ice cube is placed in the corner. How much will the water rise once the ice melts?
A 2 foot by 3 foot aquarium is filled with 9 inches of water. (2) 1 foot metal cubes are placed in opposite corners. How much will the water rise?