The Wednesday Morning Math Challenge: Week 2

I hope you enjoyed the first week of puzzles. Instead of just sending you running for your calculator, I really hope they made you think. You can find solutions to the Week 1 puzzles here, but as with most things, answers usually only bring more questions. The best part of this process is, in my opinion, the solutions — the discussion and the analysis.

This week I’ve got three new problems for you. Last week we were playing around with my favorite number. This week, well … hopefully you can figure out the common theme!

1) What is the smallest amount of money (in U.S. currency) that cannot be represented using six coins (quarters, dimes, nickels and pennies) or fewer?

2) Seven ants are placed on the top of a stick that’s one foot long. Each ant travels either left or right along the stick at a speed of four feet per minute. If two ants collide, they both reverse direction. If an ant reaches the end of the stick, it falls off. What’s the shortest amount of time you would have to wait to guarantee that there are no more ants on the stick?

3) A man flips two coins. One of the coins landed on heads. What’s the probability that the other is also heads?