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This puzzle is part of the Monthly Topic Challenge #9: Game/Quiz Shows.


"Well?" asks Howie Mandel. "Would you like to keep your case or switch it with the final one?"
You freeze in panic. How did you get into this situation?
You think back to the events that led to this conundrum...

When you were initially selected to be a contestant on the game show Deal or No Deal, you were thrilled. The day of the game came all too quickly.
As the lights shone and the camera rolled, you strode onto stage and surveyed the scene. On stage, 26 beautiful models held 26 briefcases numbered from 1 to 26. Each briefcase held a different amount of money. A video wall displayed the amounts in play (but not disclosing which case held which amount), ranging from \$4 to \$76,556,574.
"Why such strange amounts?" you asked.
"Well, it's a special puzzling edition," answered Howie. "Just remember, you don't get to see what value is in each briefcase unless you open it. And once you open a briefcase, it's out of play. Now select a briefcase to begin, and keep it closed!"
You selected briefcase #15, your favorite number. The model who held it handed it over with a smile. A good omen, you thought.
Things looked promising as the game progressed. Briefcases 17-26 were opened and contained middle-ranged dollar amounts. The four largest amounts, including the big prize of $76,556,574 were still in play!

But now, all the cases have been opened except two: Case #15, which you initially selected, and Case #16, held by the model Rocky Mindi Reese Holtan.
You need to decide if you should keep Case 15, or switch it with Case 16. And thrillingly, the big prize hasn't been found - which means it's in one of those two cases!
You definitely want to walk away with the grand prize... but which case to select? You consider what Howie said about a special puzzling edition. Cases 17-26 seem pretty random, but there is definitely some sort of pattern hidden in the first 14 cases which were opened. The dollar amounts in them are nearly in ascending order! Should you select case 16 because it's the highest number remaining? But Cases 5 and 6 don't fit the pattern... maybe you should take 15. Besides, it's hard to trust a model with two middle names...

Sweat beads on your forehead. Howie stares at you intently. "You look like you could use a hint. Here, take this." He hands you a cryptic looking crossword grid.

You contemplate the crossword and the almost-pattern you spotted in cases 1-14. What should you do? And can you complete the crossword?

Information you have gathered:

Case #  Model Name               $ Amount
1       Ti Heard                 $4
2       Ariel Evens              $6
3       Callie Alice Reynolds    $34
4       H. Pranava Middlesex     $65
5       Penny Lane               $752
6       Dot Ice Curt             $564
7       Stu D. Finglas           $7,664
8       Doctor Lira Street       $5,574
9       Hope Yafter Backrate     $75,655
10      Opal Tuccen Lost         $56,674
11      Alabama Post-Fact        $755,633
12      Stormy Emma Alchatti     $475,544
13      Paulina Comtot Windswept $5,775,553
14      Comet Love Just          $5,676,744
16      Rocky Mindi Reese Holtan 

crossword

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    $\begingroup$ Well, obviously, the probability of the first case you picked, #15, being the big prize is 1/26, whereas the probability of #16 being it, conditional on cases 1-14 and 17-26 not being it, is a significantly higher chanc...er, wait, this isn't Math.SE? right, sorry, carry on. $\endgroup$
    – Rubio
    Apr 13, 2023 at 5:49
  • $\begingroup$ So many 'al's :o $\endgroup$ Apr 13, 2023 at 12:08

1 Answer 1

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You should:

Swap for Box 16 – that’s where the big-money jackpot of $76,556,574 is!

How can we work this out? First look at the names of the people holding the boxes…

These are all examples of wordplay like you might find in a cryptic crossword clue (occasionally with some words concatenated to make it look more like a name). They can be solved as follows, noting that the number of the box in each case is actually the enumeration for the clue – the number of letters it contains:

1 Ti Heard (\$4) = “Ti” = T
2 Ariel Evens (\$6) = (-a)R(-i)E(-l) = RE
3 Callie Alice Reynolds (\$34) = CAR (by taking the person’s initials)
4 H. Pranava Middlesex (\$65) = H + OM + (-s)E(-x) = HOME
5 Penny Lane (\$752) = P (Penny) + LANE = PLANE
6 Dot Ice Curt (\$564) = ATOM (Dot) + IC(-e) = ATOMIC
7 Stu D. Finglas (\$7,664) = STU + D + ENT = STUDENT
8 Doctor Lira Street (\$5,574) = LIRA* + ROAD (Street) = RAILROAD
9 Hope Yafter Backrate (\$75,655) = PLAN (Hope) + RATE< + Y = PLANETARY
10 Opal Tuccen Lost (\$56,674) = OPALTUCCEN* = CONCEPTUAL
11 Alabama Post-Fact (\$755,633) = STATISTIC (Fact) + AL (Alabama) = STATISTICAL
12 Stormy Emma Alchatti (\$475,544) = EMMAALCHATTI* = MATHEMATICAL
13 Paulina Comtot Windswept (\$5,775,553) = PAULINACOMTOT* = COMPUTATIONAL
14 Comet Love Just (\$5,676,744) = METEOR (Comet) + O (Love) + LOGICAL (Just) = METEOROLOGICAL
16 Rocky Mindi Reese Holtan (\$UNKNOWN) = MINDIREESEHOLTAN* = THREEDIMENSIONAL

Now we can populate the crossword with these words:

Populated crossword

(Note that the 1-letter answer's position is indicated by the number 1 given in the diagram...)

Now note the boxes in yellow in the image…

These spell out the keyword BRAILLE. So we likely have to use the Braille alphabet in some capacity.

In fact, let’s spell out the first few entries using Braille and see if we can spot a pattern…

Words 1 to 4 spelled in Braille: T, RE, CAR, HOME

– ‘T’ is formed using 4 Braille dots, and its corresponding box is worth \$4.

– ‘RE’ is formed using 6 Braille dots and its corresponding box is worth \$6.

– ‘CAR’ is formed using 7 Braille dots and its corresponding box is worth \$34, whose digits sum to 7.

– ‘HOME’ is formed using 11 Braille dots and its corresponding box is worth \$65, whose digits sum to 11.

In fact, let’s drill down a little deeper into those last two…

If we split the words into pairs of letters (with an odd-one-out at the end if any leftovers), we can see that CA is spelled with 3 Braille dots, while R is spelled with 4, whilst also HO is spelled with 6 Braille dots, while ME is spelled with 5.

In other words, if we split every word into its constituent pairs of letters and count the number of Braille dots in each pair, then concatenate those numbers, we end up with the value of the prize money in the corresponding box! This is how the prize money values are all calculated. (Try it with some others to see for yourself.)

Ultimately, then, if we wish to hunt down the big-money jackpot we need to work out…

…if the value of Box 16’s ‘THREEDIMENSIONAL’ matches the jackpot’s value of 76,556,574 – if it does, we take that one; if it doesn’t, we stick with Box 15, because – whatever the model’s name – the big money must be in it!

THREEDIMENSIONAL spelled out in Braille with corresponding dot counts of letter pairs

And it does match! Quick - switch boxes to win the big money!

PS

Note that Braille - a writing system for the blind - is a very appropriate choice of obfuscation here, in a puzzle about a game show based heavily on things (i.e. prize money values) you cannot see!

Furthermore, as a nice little Easter Egg, the answers concealed in the names of the models can all precede or follow the word 'MODEL' to make a phrase:

MODEL T, REMODEL, CAR MODEL (or even MODEL CAR), MODEL HOME, MODEL PLANE, ATOMIC MODEL, MODEL STUDENT, MODEL RAILROAD, PLANETARY MODEL, CONCEPTUAL MODEL, STATISTICAL MODEL, MATHEMATICAL MODEL, COMPUTATIONAL MODEL, METEROLOGICAL MODEL, and THREE-DIMENSIONAL MODEL.

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    $\begingroup$ Spotlight on indicated by the letter 1 $\endgroup$ Apr 13, 2023 at 20:07

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