Kominers’s Conundrums: An Invention Puzzle — and That’s Not All!
(Bloomberg Opinion) -- Last week, the gadget world lost one of its heroes: inventor and salesman Ron Popeil. His series of “__-O-Matic” products, in particular, became a cultural phenomenon — especially the one that “slices” and “dices.” And his ads acquired an early form of meme status that sometimes overshadowed the genuine accessibility benefits of many of his wares.
In Ron’s honor — for a limited time only — we’re giving you the opportunity to participate in a puzzling tribute. This offer is not available in stores, so you’d better act now!
We’ve imagined five new Popeil-style inventions, each one combining two common English words into an “O”-separated pair. We’ve indicated the number of letters in each.
Your challenge? To identify the inventions!
Want melodic sounds or rocking tunes, but don’t have the money for a long-term hire? The FIVE-O-SIX employs college students over the summer.
Looking for an adorable rabbit? Look no further than this shortened web address! It’s the amazing FIVE-O-THREE!
Trying to find a new material for your stop sign? Our SEVEN-O-SIX brings together the best of eight-sided shapes and calfskin parchment!
Do you always think of things just as you’re entering or exiting the room? Then you can jot them down on our FOUR-O-SEVEN — available in both wide- and college-ruled formats.
Want to take your coiffure to the next level? Our brand-new SIX-O-FIVE will give you a bouffant that matches your long-legged paternal arachnid!
But wait, there’s more! We’ve developed our own new device: the “Carve-O-Answer,” which cuts out new words from the center o’ puzzle answers. Once you identify the five inventions above, you can use our Carve-O-Answer on them. Like a particular Popeil invention, you can “set it and forget it:” If you “set” the Carve-O-Answer correctly, you’ll be able to “forget” some of the letters in the inventions’ names in a way that leads to an instruction explaining the inventive answer you should submit this week.
And that’s not all! Once you’ve completed the main Conundrum, you can go back to the inventions and pull letters from their names — specifically, the third, fourth, first, third, second, sixth, fourth, sixth, fourth, and second letters in the different component words. Those letters may look like a runny mess at first, but you can rearrange them to obtain a bonus answer that solves the following riddle:
Which Popeil invention does every puzzle creator need?
If you manage to wow the studio audience with your solution to this Conundrum — or if you even make partial progress — our operators are standing by at firstname.lastname@example.org. Solve now! (This one-of-a-kind puzzle offer expires at midnight New York time on Thursday, August 5.)
Programming note: The next Conundrums will run on August 8.
Previously in Kominers’s Conundrums…
We presented the “Olympics of Brainteasers,” with puzzles built around three of our favorite summer Olympic sports. Solvers could “medal” in whichever sport(s) they wanted.
Up first was ARCHERY, where the scorekeeper forgot to write down which lettered arrows belonged to which competitor.
We were given the scores and rules as follows:
The first archer earned 66 points; the second earned 89.
Arrows that hit the bull’s-eye in the center are worth 10, and then the concentric rings around the bull’s-eye are worth 9, 7, 5, 3, and 1 point, respectively — starting from the inner ring and moving to the edge. Plus to make the game more intense as it goes on, there’s a special bonus rule in effect: your second shot’s point value is doubled, and your third shot’s point value is multiplied by 10.
The bonus rule meant that the total score from the second and third arrows would always be even. Moreover, each ring was worth an odd number of points. Thus, in order for the first archer to have an even score overall, they must have shot the bull’s-eye on their first shot — with the “A” arrow.
That meant the first archer’s second and third shots were worth a total of 56 points; given the bonus rule, the third arrow had to be either the “E” (for 5 × 10 = 50 points), “G” (for 3 × 10 = 30) or “O” (for 1 × 10 = 10). Only the “E” option was high enough for the second arrow to bring the total score up to 56. That left 6 points for the second arrow, corresponding to the “G” (3 × 2 = 6).
Thus the second archer must have shot the “L,” “D,” and “O.” The “L” arrow had too high a point score to have been third (9 × 10 = 90, which is higher than the second archer’s total score). From there, a bit of arithmetic could quickly confirm the full order: “O” then “L” then “D.”
Putting the arrow letters together in shot order spelled out the answer to the following riddle:
Why didn’t they allow archery in the Junior Olympics? It was too AGE-OLD.
Next was SPORT CLIMBING, where solvers had to map out the different holds and find the shortest path to the top.
Each clue described which holds could be reached from a given hold; the relationship was symmetric, so if you could reach the MARIGOLD hold from the BLUE hold, then of course you could reach the BLUE hold from the MARIGOLD hold. (That said, of course the goal was to make upwards progress — you would waste way too much energy climbing around in loops!)
The full set of clues was as follows:
From the BLUE hold at the bottom, you can reach the MARIGOLD hold, the RED hold and the UMBER hold.
From the EMERALD hold, you can reach the ZUCCHINI hold and the RAINBOW hold at the top.
From the GREEN hold, you can reach the INDIGO hold and the UMBER hold.
From the INDIGO hold, you can reach the GREEN hold, the MAROON hold and the WISTERIA hold.
From the MARIGOLD hold, you can reach the BLUE hold.
From the MAROON hold, you can reach the INDIGO hold.
From the NAVY hold, you can reach the ORANGE hold, the VERMILION hold and the ZUCCHINI hold.
From the OLIVE hold, you can reach WHITE hold and the RAINBOW hold at the top.
From the ORANGE hold, you can reach the NAVY hold, the RED hold and the YELLOW hold.
From the PUCE hold, you can reach the VERMILION hold and the WHITE hold.
From the RED hold, you can reach the BLUE hold, the ORANGE hold and the UMBER hold.
From the SEAGULL hold, you can reach the YELLOW hold.
From the UMBER hold, you can reach the BLUE hold, the GREEN hold and the RED hold.
From the VERMILION hold, you can reach the NAVY hold, the PUCE hold and the ZUCCHINI hold.
From the WHITE hold, you can reach the OLIVE hold and the PUCE hold.
From the WISTERIA hold, you can reach the INDIGO hold and the ZUCCHINI hold.
From the YELLOW hold, you can reach the ORANGE hold and the SEAGULL hold.
From the ZUCCHINI hold, you can reach the EMERALD hold, the NAVY hold, the VERMILION hold and the WISTERIA hold.
Charting out the different connections led to the following climbing wall — as illustrated by Conundrums climbing champion Lara Williams:
There were multiple routes to the “RAINBOW hold at the top,” but the fastest one started at the bottom with BLUE, then proceeded to RED, ORANGE, NAVY, ZUCCHINI, EMERALD, and RAINBOW (in that order). Looking at the first letters in these colors’ names spelled out the answer to the following riddle:
What’s the main cosmetic benefit of moving sport climbing competitions outside? The sun helps the players get BRONZER.
(Note that the answer “bronzer” is both a color pun and a cosmetic pun. We’re hilarious at Conundrums.)
The third sport was DIVING. This puzzle was a bit more cryptic than the other two: Solvers had to “find the divers in the ‘letter pool,’” given the dive types presented. At first, the puzzle looked like a classic word search, with the dive types FORWARD, BACKWARD, REVERSE, INWARD, TWISTING, ARMSTAND, STRAIGHT, PIKE, and TUCK as the “word bank” — but solvers soon realized that the dive types didn’t quite appear in the pool.
That said, some sequences of letters in the pool looked close — for example, the dive type “REVERSE” almost appeared in the bottom right corner of the pool, except it had an “I” in the middle and was missing the “E” at the end.
The trick was, as we had clued, that that there had been “a bit of displacement:” extra letters — our “divers” — had jumped into the middle of the dive types, in each case breaking up the word and displacing one letter off the edge of the pool. Realizing this made it possible to find all the suitably adjusted dive types — and their “diver” letters. (As an extra Easter egg, highlighting the dive types in the grid led to an image that looks kind of like someone jumping off a diving board. )
What’s the problem with having too many people dive at once? It makes the water SPILL OVER.
Those who solved all three individual puzzles could head over to the WINNERS’ CIRCLE for an extra challenge.
The instructions were to “collect your three medals [… and] mount the podiums pictured below.”
The image was reminiscent of the tri-level podium used for awarding Olympic medals. That fit with the reference to “medals” in the clue. But how could you use that information?
Eagle-eyed solvers noticed that the answer to each riddle contained the name of an Olympic medal. “Collecting” those medals left a few other letters, which could be placed on the podiums in medal order (from left to right: “silver,” “gold,” and then “bronze”).
AGE-OLD -> AE
BRONZER -> R
SPILLOVER -> PLO
Reading the podium letters in a zigzag order from left to right then spelled out “a prize that’s almost mythical — a worthy reward for your puzzle-solving triumph:” APOLLO’S TAPESTRY, a reference to this “Triumph of Apollo” tapestry series.
Gold medal on the podium puzzle awarded to Zoz*; silver to Franklyn Wang & Joyce Tian*; and bronze to Jennifer Walsh & Dan Rubin*!
Ross Rheingans-Yoo was the first to medal in climbing and diving; Zoz* was the first to medal in archery. The next to medal in the individual sports were Lazar Ilic, Franklyn Wang & Joyce Tian*, Ellen & William Kominers, Zarin Pathan*, Jennifer Walsh & Dan Rubin*, Adam Slomoi, Spaceman Spiff*, Anna Collins*, Kira Goldner*, Zach Wissner-Gross (a.k.a. FiveThirtyEight’s Riddler), and Mirac Suzgun. The other medalists were Mason Arbery*, Bella Beckett & Will Hartog*, Cathie Blanchard, Tony Carango, KD Dekker*, Noam D. Elkies, Andrew Garber, Yannai Gonczarowski & Elee Shimshoni*, Maya Kaczorowski*, Ganesh Natarajan, Nancy & Murray Stern*, Warren Sunada-Wong, Michael Thaler*, Nathaniel Ver Steeg*, Sanandan Swaminathan*, and Ryan Yu*. (Solvers are listed if they completed at least one of the three sports puzzles; asterisks denote those who solved the podium puzzle.) Suzgun submitted a particularly impressive solution to the sport climbing puzzle using Dijkstra’s shortest path algorithm. And thanks especially to my brother, Paul Kominers*, for test-solving!
The Bonus Round
FiveThirtyEight’s Riddler Nation goes up against Conundrum County in their own puzzle Olympics; Mark Rober’s domino-setting robot goes up against domino extraordinaire Hevesh5. A “pizza toppings” mind-game; a “four frogs” puzzle; a “Minesweeper” captcha; and a Gold-medal mathematician. Mini particle accelerators; a Renaissance Scotland time travel adventure; and touring a 1970s Tokyo arcade. Live-action Pokémon? Seizing the Epic of Gilgamesh; buying books and never reading them (hat tip: Ariel Dora Stern); moreover, “Iceland may be the tip of a sunken continent” (hat tip: Ellen Dickstein Kominers). ShinyZeni just played 100% of Super Metroid in 1:12:53, setting a new world record. Plus inquiring minds want to know: How much do Olympic athletes earn for winning medals?
You can't touch this pun game going on here at Conundrums!
Indeed, if the first archer’s third arrow had been “G,” then they would’ve needed 26 points from the second arrow, requiring an arrow score of 13 before doubling.
Emphasis on "kind of."
Did you know that the different dive types have an official order? More news you can use, courtesy of Conundrums!
This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.
Scott Duke Kominers is the MBA Class of 1960 Associate Professor of Business Administration at Harvard Business School, and a faculty affiliate of the Harvard Department of Economics. Previously, he was a junior fellow at the Harvard Society of Fellows and the inaugural research scholar at the Becker Friedman Institute for Research in Economics at the University of Chicago.
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