Renowned puzzler Peter Winkler invented the addictive word game, HIPE, with some friends when they were juniors in high school. While it may not have become the overnight success of Wordle, the game did earn Winkler admission to Harvard. According to his book, Mathematical Mind-Benders, he wrote a college admission essay about how his verbal diversion sparked a local craze. Four years later, as a Harvard senior, Winkler overheard an admissions committee member quizzing a colleague with HIPEs—and even calling them HIPEs, a name the teen inventors had coined.
The object is simple. Given a string of letters like NSW, find a word that contains those letters in order, with nothing else in between. The letter combinations often appear so unnatural that they couldn’t possibly occur in any typical English words, yet the answers are common. Have you figured out the answer to NSW? I’ve used it twice in this paragraph.
Here are two more examples. XOP = SAXOPHONE. The name of the game, HIPE, is itself a tough one: ARCHIPELAGO. This week’s puzzle presents some of my favorite HIPEs. I promise that all of the answers are common words (more common than archipelago). A great thing about HIPEs is that they can be just as fun to discover as to solve. I’d love to see new examples that you come up with. I will try to solve any HIPE posted in the comments section and will share some favorites in the answer write-up next Monday.
Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!
Puzzle #31: HIPE Me Up
For each string of letters, find a word that contains that consecutive letter sequence.
- BV
- WKW
- ONIG
- SPB
- RAOR
- HQ
- TANTAN
- PTC
- GUAG
I’ll be back next Monday with the answers and a new puzzle. Do you know a cool puzzle that you think should be featured here? Message me on X @JackPMurtagh or email me at gizmodopuzzle@gmail.com
Solution to Puzzle #30: Survivor flags
Did you win immunity for your tribe in last week’s real Survivor puzzle? Shout-out to Mike Webb for emailing me a nicely algorithmic presentation of the solution.
The team that goes first can always force a win. Thinking backwards makes this easier to solve. If it’s ever your move and only one, two, or three flags remain, then you’ve won because you can take all of the remaining flags. But if four flags remain on your turn, then you’re in trouble, because no matter how many you take, the opposing tribe will be able to win on the next move.
So our intermediate goal will be to make four flags remain when the other tribe is to move. If it’s our move when five, six, or seven flags remain, then we win by taking one, two, or three flags, respectively, leaving our opponents with four. But again if it’s our turn with eight flags remaining then we’re in trouble, so we’d also like it to be the opponent’s turn when eight flags remain. When we keep thinking like this, a pattern emerges: the team to move when the remaining number of flags is a multiple of four (four, eight, 16, or 20) loses.
So Tribe A wins by taking one flag on their first move, leaving 20. Then no matter how many flags Tribe B takes, Tribe A will take a complementary number to reach the next multiple of four, e.g. if Tribe B takes three flags, then 17 remain, and Tribe A will take 1. Proceeding this way, Tribe A can always make it Tribe B’s turn when a multiple of four flags remain and can force a win.
Contestants in the real show did not figure this out, and in fact most of their moves throughout the game handed the winning advantage to the opposing team (who didn’t know what to do with it and handed it right back). The team that went first ended up losing. You can watch the drama here.
Renowned puzzler Peter Winkler invented the addictive word game, HIPE, with some friends when they were juniors in high school. While it may not have become the overnight success of Wordle, the game did earn Winkler admission to Harvard. According to his book, Mathematical Mind-Benders, he wrote a college admission essay about how his verbal diversion sparked a local craze. Four years later, as a Harvard senior, Winkler overheard an admissions committee member quizzing a colleague with HIPEs—and even calling them HIPEs, a name the teen inventors had coined.
The object is simple. Given a string of letters like NSW, find a word that contains those letters in order, with nothing else in between. The letter combinations often appear so unnatural that they couldn’t possibly occur in any typical English words, yet the answers are common. Have you figured out the answer to NSW? I’ve used it twice in this paragraph.
Here are two more examples. XOP = SAXOPHONE. The name of the game, HIPE, is itself a tough one: ARCHIPELAGO. This week’s puzzle presents some of my favorite HIPEs. I promise that all of the answers are common words (more common than archipelago). A great thing about HIPEs is that they can be just as fun to discover as to solve. I’d love to see new examples that you come up with. I will try to solve any HIPE posted in the comments section and will share some favorites in the answer write-up next Monday.
Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!
Puzzle #31: HIPE Me Up
For each string of letters, find a word that contains that consecutive letter sequence.
- BV
- WKW
- ONIG
- SPB
- RAOR
- HQ
- TANTAN
- PTC
- GUAG
I’ll be back next Monday with the answers and a new puzzle. Do you know a cool puzzle that you think should be featured here? Message me on X @JackPMurtagh or email me at gizmodopuzzle@gmail.com
Solution to Puzzle #30: Survivor flags
Did you win immunity for your tribe in last week’s real Survivor puzzle? Shout-out to Mike Webb for emailing me a nicely algorithmic presentation of the solution.
The team that goes first can always force a win. Thinking backwards makes this easier to solve. If it’s ever your move and only one, two, or three flags remain, then you’ve won because you can take all of the remaining flags. But if four flags remain on your turn, then you’re in trouble, because no matter how many you take, the opposing tribe will be able to win on the next move.
So our intermediate goal will be to make four flags remain when the other tribe is to move. If it’s our move when five, six, or seven flags remain, then we win by taking one, two, or three flags, respectively, leaving our opponents with four. But again if it’s our turn with eight flags remaining then we’re in trouble, so we’d also like it to be the opponent’s turn when eight flags remain. When we keep thinking like this, a pattern emerges: the team to move when the remaining number of flags is a multiple of four (four, eight, 16, or 20) loses.
So Tribe A wins by taking one flag on their first move, leaving 20. Then no matter how many flags Tribe B takes, Tribe A will take a complementary number to reach the next multiple of four, e.g. if Tribe B takes three flags, then 17 remain, and Tribe A will take 1. Proceeding this way, Tribe A can always make it Tribe B’s turn when a multiple of four flags remain and can force a win.
Contestants in the real show did not figure this out, and in fact most of their moves throughout the game handed the winning advantage to the opposing team (who didn’t know what to do with it and handed it right back). The team that went first ended up losing. You can watch the drama here.