Problem
Asta, Bronya, and Clara all have different numbers of cats. They had the following conversation: … [statements with truth/lie rules based on who has more cats]. What is the number of cats Bronya has?
Problem
Two friends canoe upstream for 4 hours, then downstream for 5 hours. The next day, they canoe 23 miles upstream and arrive at 16:00. The river flows at 2 mph. What time did they leave?
Problem
You baked 5 indistinguishable snickerdoodle cookies and 7 indistinguishable chocolate chip cookies. Compute the number of ways to arrange 6 of these cookies into a straight line.
Problem
Three cats are competing in a jumping contest. The most athletic cat wins with probability 3/5, the least athletic cat wins with probability 1/10, and the remaining cat wins with probability 3/10. I picked a cat uniformly at random to cheer on but it did not win. Compute the probability I picked the most athletic cat.
Problem
A spinner has three regions, and the probabilities of landing in each region are 1/6, 1/6, 2/3. Compute the expected number of spins it would take to land in two distinct regions.
Problem
A gardener is waiting for two flowers to bloom. One blooms at a random time in 30 days and stays for 9 days. The other also blooms randomly and lasts 12 days. What’s the probability they overlap?
Problem
In the figure below, place a building with 1, 2, 3, or 4 floors in each cell such that no two buildings in a row or column have the same number of floors. In addition, the number of visible buildings, as viewed from the direction of each number outside the grid, is equal to the value of that number. Note that taller buildings block shorter buildings located behind them.
What is the number of floors in the buildings in the cells labeled A and B?
Express your answer as a two-digit integer AB.
Problem
A deck contains eight cards: two 10s, two Js, two Qs, two Ks. You are dealt five cards without replacement from this deck.
Compute the expected number of pairs in your hand.
Express your answer as a fraction in simplest form. Enter the numerator in the first blank and the denominator in the second blank.
Problem
Suppose you have 3 tokens for a betting game and your goal is to bring your fortune up to 5 tokens before running out of tokens.
You devised a bold betting strategy where every turn, you will bet as many tokens as possible against the house but not any more than necessary to bring you to 5 tokens.
You always have a probability of 3/4 to win the bet.
Compute the probability you reach 5 tokens before running out.
Express your answer as a fraction in simplest form.
Problem
A robot moves from (0,0) to (4,6) using only steps R (right) and U (up), but cannot take 3 steps in a row in the same direction.
How many such paths are there?
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