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2021-2022
Archived Problems of the Week
Solutions
POW #1: Apples, Oranges and Bananas There are 15 different ways to make 7 fruits, with some being apples, oranges and bananas. POW#2: Playing Fetch In total Spencer, the dog, ran 70 meters (8 + 16 + 11) + (8 + 16 + 11). POW #3 Repeating Pattern The 15th object in the pattern would be the triangle. The 28th object would be the down arrow and the 101st object would the blue up arrow. POW #4: Pumpkins Full of Coins The large pumpkin with nickels hols the most money because it holds $4.35 which is more than the others.
The XL pumpkin has $4.00 in pennies. The small pumpkin has $4.30 in dimes, and the mini pumpkin holds $4.25 in quarters.
POW #5: Birthday Candles There would be 36 total candles on the cake (1+2+3+4+5+6+7+8). POW #6 Sweet Possibilities There are 48 possible combinations of dessert options. POW #7 Jumping Frogs Both frogs would land on lily pads #6, 12, 18, 24, 30 and 36. POW #8 Ocean Legs If I saw BOTH crabs and starfish, then I could see 2 crabs (20 legs) and 2 starfish (10 legs) or I could see 1 crab (10 legs) and 4 starfish (20 legs). POW#9: Palindrome Dates There are 10 different dates if you write month-day-year (2/2/22, 2/20/22, 2/21/22, 2/22/22, 2/23/22, 2/24/22, 2/25/22, 2/26/22, 2/27/22 and 2/28/22). If you write day/month/year, then there are 9 dates (22-1-22, 22-3-22, 22-4-22, 22-5-22, 22-6-22, 22-7-22, 22-8-22, 22-9-22, 22-11-22). There are numerous ways to represent 100 in an array or a triangle. Some solutions include single layer rectangles: 2x50, 4x25, 5x20, 10x10 or 100 x 1. One triangle solution was an isosceles triangle with a base of 19 apples and a height of 10 apples. Some students stacked the 100 apples into a rectangular prism shap (e.g., 5 layers of 20 (10x2) or 4 layers of 25 (5x5)). Thank you! Yes, all 4 triangles have the same area, so the rectangle is divided into four equal parts or fourths. There are 36 different ways to put 10 crayons with some crayons being red, blue, and green. 4 students liked neither peanut butter nor jelly. On Monday, Angela ate 8 grapes. There are 3 different ways to move ONLY 2 circles to make Picture 2: 1) Move A and E; 2) Move C & D; 3) Move B and F. Charlie began with a bag of 120 gumballs. Adam needs $4.00. He could save 16 quarters OR 14 quarters and 5 dimes, OR 12 quarters and 10 dimes OR 10 quarters and 15 dimes, OR 8 quarters and 20 dimes OR 6 quarters and 25 dimes, OR 4 quarters and 30 dimes or 2 quarters and 35 dimes OR 40 dimes (9 combinations).
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