Logo Shot

In the expression LOGO + SHOT = HARD, each letter represents a single digit number from 0 to 9. Different letters represent different numbers. L, S and H cannot be zero. What's the difference between the largest and smallest values of HARD?

Running drill

Starting at the same time on opposite baselines of a basketball court, Dr. Hong and Leo cross back and forth for 35 seconds without stopping. Dr. Hong needs 5 second to cross court, while Leo needs 7 seconds. What is the number of times during the 35 seconds that the Dr. Hong passes Leo going in the same or opposite direction?

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A similar problem was given in Assignment 1 of Charlotte Math Meetup:

Starting at the same time on opposite shores of a lake, two boats cross back and forth for 35 minutes without stopping. One boat needs 5 minutes to cross the lake. The other boat needs 7 minutes. What is the number of times during the 35 minutes that the faster boat passes the slower boat going in the same or opposite direction?

1v1 Basketball

Dr. Hong and Leo play a series of 1v1 basketball games until one of them has won two games. No game ends in a tie. In any single game, the probability that Dr. Hong wins is 80%. What is the probability that they play exactly 2 games?

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A similar problem was given in Assignment 1 of Charlotte Math Meetup:

Team A and Team B play a series of games until one of them has won two games. No game ends in a tie. In any single game, the probability that Team A win is 70%. What is the probability that they play exactly 2 games?

3x3 Basketball Teams

Leo and 8 other kids are shooting around in the gym. They decide to play 3x3 pickup games. They want to split up in to 3 teams, with 3 players on each team. How many different ways can they split the group?