## ________________

The team captain, Adrian, has two probability puzzles to share with the others.

## ________________

### Roll Those Bones

You keep rolling a set of five regular dice until you get a set showing exactly one six or a set showing no sixes. When that happens, you stop rolling the dice. You win if you stop on a roll with exactly one six. You lose if you stop on a roll with no sixes.

*What is your probability of winning?*

### Keeping Things Even

Jones and Brown are planning a paintball duel. They agree to take turns shooting at each other until someone has been hit. Jones, who can hit Brown in a single shot only 40% of the time, is allowed to go first.

*If the duel favors neither, what is Brown’s probability of hitting Jones in a single shot?*

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## Solutions to week 127

To get to your gate in the shortest time possible for Race to the Gate, you should tie your shoe on the walkway. In Tricky Logic Game, anyone who sees HH or TT should guess the opposite letter; otherwise, that person should pass. This strategy loses only if all three have the same letter – a 25% chance. This gives them a 75% chance of winning the prize.

**Race to the Gate answer explained:**

You should tie your shoe on the walkway. On the walkway, you spend the 30 seconds it takes tying your shoe making the progress of the walkway. Off the walkway you make no progress.

## Recent Weeks

**Week 127**: Race to the Gate & Tricky Logic Game, solutions to Logical Coffee Order & Here’s Looking at You

**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

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

**Come back next week** for answers and more puzzles.