Solution to the Peppermint Patty Brain Teaser!

[Image courtesy of SharpBrains.com.]

A week ago, we shared a brain teaser sent in by a PuzzleNationer named Bethany, who challenged us to solve the following stumper.

Today, we’re going to share not only the solution, but how we got there! Please enjoy this brief solve and tutorial, inspired by one of your fellow PuzzleNationers!


The Peppermint Patty Riddle

You’re facing your friend, Caryn, in a “candy-off,” which works as follows: There’s a pile of one hundred caramels and one peppermint patty. You and Caryn will go back and forth taking at least one and no more than five caramels from the candy pile in each turn. The person who removes the last caramel will also get the peppermint patty. And you love peppermint patties.

Suppose Caryn lets you decide who goes first. Who should you choose in order to make sure you win the peppermint patty?


When I posted this brain teaser, I said that “the question basically demands that you not only achieve victory, but figure out how to do so with your very first move.”

That was meant to be a hint. Because the best way to unravel this riddle is to start at the end.

Look at the last turn. If there are five or fewer caramels left on the board and it’s Caryn’s turn, she wins. For you to guarantee a win, she needs to see six caramels on her last turn. (Seven or more allows her to take just enough to leave YOU with six, which means she wins on her next turn.)

And that six is the magic number. Her previous turn, you need to leave her with 12 caramels. The turn before that, 18 caramels. The turn before that, 24. And so on and so on.

Why? Simple.

caramel

Let’s look at the 12 caramel turn. If she takes any number of caramels (anywhere from 1 to 5), she’ll leave you with between 11 and 7 caramels. You can use your turn to remove whatever number of caramels are necessary (anywhere from 5 to 1) to leave her with six.

The entire game can be broken into six-caramel increments.

And the closest multiple of 6 to 100 (your starting point) is 96 caramels.

Which means you can’t let Caryn go first. You need to remove 4 caramels on your first turn, and then use every subsequent turn to ensure Caryn faces a multiple of six, which eventually gives you the victory and the peppermint patty.

So the answer to the riddle is you should go first.

Diabolical!

Did you solve the brain teaser, fellow PuzzleNationer? Or do you have a brain teaser you’d like us to unravel with you? Let us know in the comments section below! We’d love to hear from you.


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These Are Some Sweet Puns!

Oh yes, it’s that time again! It’s time to unleash our puzzly and punny imaginations and engage in a bit of sparkling wordplay!

You may be familiar with the board game Schmovie, hashtag games on Twitter, or the Hashtag Wars segment that used to run on @midnight on Comedy Central.

For years now, we’ve been collaborating on puzzle-themed hashtag games with our pals at Penny Dell Puzzles, and this month’s hook was #PennyDellPuzzleSweets, mashing up Penny Dell puzzles with all sorts of sweets, candy, desserts, and anything else that satisfies your puzzly sweet tooth!

Examples include: Four Candy Corn-ers, Twix and Mingle, and Ice Cream Dell Sundae Crosswords.

So, without further ado, check out what the puzzlers at PuzzleNation and Penny Dell Puzzles came up with!


Kit Kategories

Letter Skor

Middle of the Rocky Road

Tootsie Roll of the Dice / Swiss Roll of the Dice / Rolo of the Dice

Top to Black Bottom Pie

Pineapple Ups and Downs Cake

Petit Foursomes / Finish the Petit Fours / Petit Four Square

Ladyfiggurits

Key Line’ Em Up Pie / Keyword Lime Pie

Point the Milky Way / Right of Milky Way

Little Twizzlers

Everlasting Gobstoplines

Double Fudge Delight

Flan Words

Wacky Nerds

Pecancellations Pie

Animal Crackers

Starspell Burst / Starburst Words / Lucky Starburst

Starbursts and Airheads

Airheads and Tails

LemonHeads & Tails

Jigsaw Lemon Squares / Lemon Squares / Circles in the Lemon Square

Lemon Drop-Ins / Lemon Dropouts

GumDrop-Ins / Gum Drop-Outs

Puzzle Derby Pie

Chess Words Pie

Quotagraham Crackers / Quotagrahams / Graham Crackers

S’more AnaGraham Crackers, please!

S’moremaster

Carry-Turnovers

Tart and Finish

Hub-Sno-Caps

Bottle HubCaps

Family Pies

Parfait Fit

Around the Black Forest Cake

Bit-o-Honeycombs

Bits o’Honey & Reese’s Pieces

Reese’s Piece by Pieces

Pie of Diamonds

Rapid GingerbReader House

100 Grand Tour

Wonka’s Whipple Scrumptious Fudgemallow Double Delight Chocolate

ZigZagNut Candy Bar

Piggybakes Cheesecakes

Three to One Musketeer / Three Musketeers of a Kind

Cannoligrams Plus

Diamond Ringpops / Diamond Ring-Dings

Ring-Dingers / Ring Ding Master

Ring Pop Master

Doublemint Trouble Gum

Neccodewords Wafers

Fancy Give and Take Fives

Chicletterboxes

Cryptic-Tac Crossword

Spellbounty Bar

Puzzle Twin Bing

Banana Split Personalities / Banana Split and Splice

Sudo-Kudos

Make the Confection

Anagram Magic Cookie Squares

Hot Cross Sums

Chunky Mon-Keyword

Double Bubble

Ice Cream Sudoku

Do-Si-Doku

Kakoreo

Ka-churro

Creme BRoulette

Cream Fill-In

Mousse Tile

Frostics

Here & Eclair

Give and Bake

Stepping Scones

Mixed Twixes / Twixed Sixes

Caramelflage

Jell-O-Gram

Tart Game

One and Sconely

Chips Ahoy!

GhirarDELLi Logic Problems

DileM&Ma: Which color to eat first

Dim Sum-doku


Have you come up with any Penny Dell Puzzle Sweets entries of your own? Let us know! We’d love to see them!

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