Varsity Math, Week 127

Varsity Math 127

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Fresh from a recent trip to an out-of-town math competition, the coach shares a couple of problems with the team.

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Race to the Gate

As you hurriedly walk to your gate in the airport, you realize that you must stop for 30 seconds to tie your shoe. A moving walkway is in view ahead of you. You walk at a constant speed relative to the ground or walkway when you are walking.

Should you wait to tie your shoe while on the walkway, or does it matter in getting to your gate at the earliest time?

Tricky Logic Game

Three team members are assigned H or T on their foreheads, based on the toss of an unbiased coin. Each sees the others’ letters but not their own. No communication is allowed, but each must simultaneously guess their own letter or pass. They share a large prize if no one guesses incorrectly and at least one guesses correctly. After hearing the game rules but before the letters are placed, the players are allowed a strategy session.

What strategy should they use to maximize their chances of winning, and what is their probability of sharing the prize?

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Solutions to week 126

In Logical Coffee Order, only Kayla should be served coffee. The answer to Here’s Looking at You is “Yes.”

Logical Coffee Order answer explained:
Only Kayla should be served coffee. If any of the others wanted coffee, they would have answered “Yes.”

Here’s Looking at You answer explained:
If Zoe is married, then she is looking at Joshua. If Zoe is not married, then Adam is looking at her.

Recent Weeks

Week 126: Logical Coffee Order & Here’s Looking at You, solutions to Piece of Pi & Making 17 and 27

Week 125: Piece of Pi & Making 17 and 27, solutions to Cutting the Triangle & Square Repair

Week 124: Cutting the Triangle & Square Repair, solutions to Mining Mishap & Pulley Puzzle

Week 123: Mining Mishap & Pulley Puzzle, solutions to Minimum Racket Wear & Rolling Circles

Week 122: Minimum Racket Wear & Rolling Circles, solutions to Tennis Exhibition & Losing Streak

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

Come back next week for answers and more puzzles.