Feb 15, 2021
Madison Math Circle
Providing Madison children with a friendly environment that fosters learning beautiful mathematical theories beyond the regular school curriculum and developing critical thinking and problem solving skills.
Video of the Week
Weekly Riddles
1) Make a day-of-the-month calendar made of wooden blocks. There are two six sided wooden cubes, and by choosing which face is displayed for the two of these, all possible monthly dates (from 01, 02, …, to 29, 30, 31) can be displayed; note the single digit dates must start with a 0.
Your job is to write one digit (from 0, 1, 2, …, 8, 9) on each face of the two cubes so that this can be done. Good luck!
Bonus question: how many distinct solutions are there?
2) A game designer must decide how to color five buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted exactly one color. Any two neighboring buildings must be different colors, and the first, third, and fifth buildings must be different colors. How many ways are there to paint the five buildings?