Devilish Puzzle for Monday: Unraveling the Intricate Hat Trick Enigma
Hey there! It's been an exciting journey solving puzzles together every week, but it's time for the Gizmodo Monday Puzzle to take a break. A big thank you to everyone who participated, commented, or kept up with the puzzle in silence. If you're craving for more brain teasers, check out these puzzles I recently created for the Morning Brew newsletter:
- An unconventional mini crossword that will challenge your wits
- A full-sized crossword with a tricky theme designed to exercise your mind
- A new code breaking puzzle named Decipher to test your decoding skills
I also write a series on fascinating math mysteries for Scientific American, where I share intriguing math stories and puzzles for a non-math audience. If you found the preface enticing, prepare for more mind-blowing math mysteries at Scientific American.
Stay connected with me on X @JackPMurtagh as I continue to create thought-provoking puzzles and share some mind-bending math tales.
Cheers, Jack
Puzzle #48: Hat Trick Solution
Did you survive last week's dystopian extravaganza? A big shout-out to bbe for correctly solving the first puzzle and to Gary Abramson for providing an incredibly concise solution to the second puzzle.
- In the first puzzle, the group can ensure that all but one person survives. The individual at the back has no information about their hat color. Instead, they will use their only guess to convey enough information so that the remaining nine people can deduce their own hat color for certain.
The person in the back will count up the number of red hats they see. If it's an odd number, they'll shout "Red," and if it's an even number, they'll shout "Blue." Now, let's see how the next person deduces their hat color. They see eight hats. Suppose they count an odd number of reds in front of them. They realize the person behind them saw an even number of reds (since the person behind them would've shouted "Blue"). With this information, they deduce that their hat must be red to make the total number of reds even. The next person also knows whether the person behind them saw an even or odd number of red hats and can make the same deductions for themselves.
- For the second puzzle, we'll share a strategy that ensures the entire group survives unless all 10 hats happen to be red. The group only needs one person to guess correctly and one wrong guess automatically leads to the group's demise. Once one person guesses a color (declines to pass), then every subsequent person will pass. The goal is for the blue hat closest to the front to guess "Blue" and for all the rest to pass. To achieve this, every participant will pass unless they only see red hats in front of them (or if someone behind them has already guessed).
To grasp why this works, realize that the person at the back will pass unless they see nine red hats. In such a case, they'll guess blue. If they say blue, all other participants pass, and the group wins unless all ten hats are red. If the person at the back passes, that means they saw some blue hat ahead of them. If the second-to-last person sees eight reds in front of them, they understand they must be the blue hat and can guess blue. Otherwise, they'll pass. Everyone passes until a person towards the front of the line only sees red hats or no hats (if standing at the front of the line). The first person in this situation guesses blue.
The probability of all ten hats being red is 1/1,024, so the group wins with a probability of 1,023/1,024.
Enrichment Data:
Mini Crossword
- Easy Clues First: Start with short answers or common words to fill in the grid quickly.
- Word Patterns: Look for common prefixes, suffixes, or word patterns to help fill in the blanks.
- Work from the Edges: Filling in words on the edges helps you figure out adjacent words.
Full-Sized Crossword with a Tricky Theme
- Identify the Theme: Most puzzles feature a theme, so discover the repeating pattern or look for clues hinting at a central idea.
- Focus on Intersections: Words that intersect multiple other words are crucial. Solve these first to unlock more of the puzzle.
- Use Crossword Dictionaries: Refer to a crossword dictionary if you're stuck with less common words.
Decipher
- Patterns: Decipher puzzles often involve patterns or codes. Identify any repeating sequences or patterns in the text.
- Frequency Analysis: In substitution ciphers, common letters like E, T, and A appear frequently. Use this to guess substitutions.
- Work from Knowns: Leverage known letters to deduce other letters.
Mathematical Curiosities
- Understand the Concept: Math mysteries typically involve clever applications of mathematical principles. Familiarize yourself with the underlying math.
- Break Down Problems: Solve complex problems by dividing them into simpler components.
- Practice and Review: Regularly working with various mathematical concepts can help you recognize patterns and solve puzzles more effortlessly.
1.The future of puzzles looks bright as Jack Murtagh, the creator of Gizmodo Monday Puzzle, continues to create thought-provoking puzzles and shares mind-bending math tales on his X @JackPMurtagh.2. Jack's latest creations for the Morning Brew newsletter offer a mix of challenging mini crosswords, intricate full-sized crosswords with tricky themes, and new code breaking puzzles named Decipher, all designed to test one's decoding skills and mental acuity.3. For science enthusiasts, Jack's series on fascinating math mysteries for Scientific American promises more mind-blowing math mysteries that explore the boundaries of mathematics and leave readers in awe.4. Staying connected with Jack's work impressively allows individuals to gain insights into puzzles, math curiosities, and future technological advancements, all through his engaging and informative writings.
