Varsity Math, Week 111

Varsity Math 111

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This week, the coach has some Halloween puzzles for the team.

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Pumpakins

Pumpkin Crop

Having sorted them by weight, a grower takes his crop of pumpkins to the market. He sells the 42 lightest pumpkins to a customer and notes that they account for 25% of the total weight. He sells the 50 heaviest pumpkins to another customer and notes that they account for 30% of the total weight.

How many pumpkins were originally in the crop?

The Halloween Goblin

The coach poses the following question: Imagine 47 partygoers, including yourself, are trapped by a goblin. You are all brought into a dark room, where the goblin puts one of 47 different cards from a standard deck of 52 playing cards on each of your foreheads, then turns on the light and asks you each in turn, “What card is on your forehead?” You see the cards on all foreheads but your own and hear the answers of those before you. When you are questioned, you may only respond with the name of a card. Those who say the name of their card go free.

If you are allowed to confer with the others in the group before the cards are placed, what is the maximum number of the group you can guarantee will be released?

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Solutions to week 110

In Making 25, 4×6+1 and 4/.16 both equal 25. In Two Ways to 32, .5-7/4 and 5×(7-.6) both equal 32.

Making 25 answer explained:
Here are two ways to make 25 using 1, 4, and 6:
4×6+1 = 24+1 = 25
4/.16 = 25

Two Ways to 32 answer explained:
Here is one way to make 32 using 4, 5, and 7:
.5-7/4 = 1/.57/4 = 27/4 = 128/4 = 32
Here is one way to make 32 using 5, 6, and 7:
5×(7-.6) = 5×6.4 = 32

Recent Weeks

Week 110: Making 25 & Two Ways to 32, solutions to Commuters’ Dilemma & Construction Conundrum

Week 109: Commuters’ Dilemma & Construction Conundrum, solutions to Nine Coins & Five Questionable Coins

Week 108: Nine Coins & Five Questionable Coins, solutions to Ten from Two & Triangular Boundary

Week 107: Ten from Two & Triangular Boundary, solutions to Simple Multiple & Small and Simple

Week 106: Simple Multiple & Small and Simple, solutions to Math for the Ages & Three Racers

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.