Archived Problems of the Week
56 blocks were used to make the tower.
See the bulletin board for possible solutions
Solution to MPOW #1: Fun with 2017!
b) No, 2017 has only 6 digits in base 4.
c) 1,008 and 1,009
You can make $12 with 2 bills and 8 coins in a variety of ways. Here are the ways Pierce students suggested:
- two $5.00 bills and eight quarters
- two $5.00 bills and 2 half-dollar coins, 3 quarters, 2 dimes and 1 nickels
- one $10.00 bill and one $1.00 bill, 3 quarters and 5 nickels
- one $10.00 bill and one $1.00 bill, 2 quarters, 4 dimes and 2 nickels
if you have $2.00 bill then
- two $2.00 bill and eight dollar coins
- one $5.00 bill, one $2.00 bill and 4 dollar coins and 4 quarters
Solution for MPOW #2: It's a Math Party!
a) 40 handshakes
b) The mathematician's children were aged 3, 3, and 8.
13 out of the 15 people can get off the ship before it sinks.
See the POW board by the front office for solutions.
Solutions to MPOW #3: Fence Me In
a) There are 18 possible products.
b) The largest possible area is 81 square units.
c) The minimum number of rectangles needed is 6.
Due to different interpretations of the story, we are accepting 2 correct answers.
1. If you assumed that there were 4 people sharing 7 pizzas, then each person would receive 1 and 3/4 of a pizza.
2. If you thought that only 3 friends were sharing the 7 pizzas, then each person would get 2 and 1/3 pizzas.
Solutions to MPOW #4: Goody Goody Gumdrops
a) A triangle requires 3 colors. A square requires 2 colors. And a pentagon requires 3 colors.
b) Every two-dimensional shape with an odd number of sides will need 3 colors like the triangle and pentagon, while every two-dimensional shape with an even number of sides will need only 2 colors like the square.
c) The cube requires the fewest colors, as it is made up of two squares - each of which only requires two colors and they can be connected so different colors connect. The triangular pyramid requires the most colors because every corner is connected to every other corner, so it requires 4 colors - a different color for each corner.