Answers to Problems of the Week - November 15 to November 21

Rewards for Problems of the week:

5 stars for the correct answer at your level; 10 stars for the next level; 20 stars for 2+ levels up.

Lower Elementary:

Question: Ethan is making a friendship bracelet with colored beads. The beads follow the pattern red, orange, yellow, green, blue, purple, red, orange, yellow, green, blue, purple, and so on. What color is the 26th bead on the bracelet?

Answer:  Orange

Solution:  There are 6 colors in the pattern. Since the sixth color in the pattern is purple, we can count by sixes to find all the purple beads in the pattern: the 6th is purple, the 12th is purple, the 18th is purple, and the 24th bead is purple. Now, since 26 is 2 after 24, we count the next two colors in the pattern: red and orange. The 26th bead is orange.

 

Upper Elementary:

Question: A small bowl can hold 12 apples. A large bowl can hold 20 apples. If Benjamin has 132 apples and already has 6 small bowls, how many large bowls does he need for the rest of the apples?

Answer:  3 large bowls

Solution:  Benjamin already has enough small bowls to hold 12 × 6 = 72 of the 132 apples. That means that he needs enough bowls to hold 132 – 72 = 60 more. Since a large bowl holds 20 apples, he needs 60 ÷ 20 = 3 of them.

 

 Middle School:

Question: Laura K has 6 less than 3 times the number of marbles that Laura P has. Laura P has 2 more than half as many marbles as Laura W. If Laura W has 12 marbles, then how many marbles does Laura K have?

Answer:  18 marbles

Solution:  Since Laura W has 12 marbles and two more than half of 12 is 8, Laura P has 8 marbles. Six less than 3 times 8 is 18, so Laura K has 18 marbles.

 

Algebra and Up:

Question: Bryan has two snow globes. The glass sphere of the larger snow globe has a radius 3 times that of the smaller snow globe. If the larger snow globe’s glass sphere has a volume of 972π cubic centimeters, then what is the volume of the smaller snow globe’s glass sphere?

Answer:  36π cubic centimeters

Solution:  The volume of a sphere is V = ⁴/₃πr³.The large globe has a volume of 972π cubic cm, so we have 972π = ⁴/₃πr³. If we solve for r, we find the radius of the large globe is 9 cm. Since the radius of the large globe is 3 times that of the small globe, the small globe must have a radius of 3 cm. This means that the small globe has a volume of ⁴/₃π(3)³ = 36π cubic cm.

 

Challenge problem to take home. 5 stars for the correct answer. 

The following 5 keys are for the following 5 locked padlocks.

Each key opens one and only one padlock. Different keys open different padlocks. What is the least number of trials needed to guarantee that you will open all 5 padlocks?

Answer: 15 trials