Tag Archives: deduction problem

Solution to the Peppermint Patty Brain Teaser!

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[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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Another Brain Teaser Submitted by Readers For Your Puzzly Pleasure!

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[Image courtesy of SharpBrains.com.]

When’s the last time you had your brain properly tied in knots by a riddle?

That’s a pretty common occurrence around here, honestly. In our puzzly explorations of the world, we stumble across all manner of brain teasers, riddles, logic puzzles, math problems, mind ticklers, deduction games, and wordplay-fueled bits of linguistic legerdemain.

Sometimes, we even receive them directly from our fellow PuzzleNationers!

And on those occasions, we happily share them with you, dear reader, so that you can also enjoy the challenge of unraveling whatever fiendish puzzly conundrum has been placed before us.

This time around, a solver named Bethany submitted this riddle she found online. It’s known as the Peppermint Patty Riddle.

Let’s see how we do.

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?

Now that’s interesting, because it doesn’t ask us specifically HOW to achieve victory. But the question basically demands that you not only achieve victory, but figure out how to do so with your very first move.

Tricky indeed.

Will you be accepting this puzzly challenge from a fellow PuzzleNationer? Let us know in the comments section below. We’d love to hear from you!

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Solution to the Smith-Jones-Robinson Problem!

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[Image courtesy of SharpBrains.com.]

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

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 Smith-Jones-Robinson Problem

Every fact is important. The puzzle is as follows:

On a train, three men named Smith, Jones, and Robinson are the fireman, brakeman, and engineer, but not necessarily in that order. Also on the train are three businessmen who have the same names as the train crew. They will be referred to as Mr. Smith, Mr. Jones, and Mr. Robinson.

  • Mr. Robinson lives in Detroit.
  • The brakeman lives exactly halfway between Chicago and Detroit.
  • Mr. Jones earns exactly $20,000 per year, paid in thousand-dollar bills.
  • The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman, and is also paid in thousand-dollar bills.
  • Smith beats the fireman at billiards.
  • The passenger whose name is the same as the brakeman’s lives in Chicago.

From the information listed above, can you figure out the name of the engineer?

ticket to ride

We’re given one exact number, so let’s start there.

The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman. Mr. Jones earns exactly $20,000 per year, which cannot be divided evenly by three (in thousand dollar bills), so Mr. Jones is NOT the brakeman’s nearest neighbor.

The brakeman lives exactly halfway between Chicago and Detroit, and Mr. Robinson lives in Detroit, so Mr. Robinson cannot be the passenger who lives nearest to the brakeman. And as we just determined, Mr. Jones is also not the brakeman’s nearest neighbor. That leaves Mr. Smith as the brakeman’s nearest neighbor.

This tells us about the passengers, but how does it help us with the train crew?

Well, the passenger whose name is the same as the brakeman’s lives in Chicago. And neither Mr. Robinson nor Mr. Smith (who is nearest to the brakeman) can live in Chicago. That tells us Mr. Jones lives in Chicago.

This means that the brakeman’s name is Jones.

We can finally turn our attention to the train crew now.

Now that we know the brakeman’s name is Jones, that leaves only Smith and Robinson as possibilities. And we know that Smith beats the fireman at billiards. Smith can’t be the fireman or the brakeman, so Smith must be the engineer.

Did you identify the engineer and outwit the Smith-Jones-Robinson Problem? Let us know in the comments section below. We’d love to hear from you!

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Another Brain Teaser Submitted For Your Puzzly Pleasure!

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[Image courtesy of SharpBrains.com.]

A few weeks ago, we shared two brain teasers submitted by one of our fellow PuzzleNationers! Well, that must have inspired some of the readership, because we received another brain teaser to solve and share this week!

This brain teaser, submitted by puzzle fan Brian, is called The Smith-Jones-Robinson Problem, and Brian says it has been slightly altered from the original for clarity’s sake.

So, without further ado, let’s get to the puzzle! (We’ll share the solution next week!)

The Smith-Jones-Robinson Problem

Every fact is important. The puzzle is as follows:

On a train, three men named Smith, Jones, and Robinson are the fireman, brakeman, and engineer, but not necessarily in that order. Also on the train are three businessmen who have the same names as the train crew. They will be referred to as Mr. Smith, Mr. Jones, and Mr. Robinson.

  • Mr. Robinson lives in Detroit.
  • The brakeman lives exactly halfway between Chicago and Detroit.
  • Mr. Jones earns exactly $20,000 per year, paid in thousand-dollar bills.
  • The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman, and is also paid in thousand-dollar bills.
  • Smith beats the fireman at billiards.
  • The passenger whose name is the same as the brakeman’s lives in Chicago.

From the information listed above, can you figure out the name of the engineer?

Will you be accepting this puzzly challenge from a fellow PuzzleNationer? Let us know in the comments section below. We’d love to hear from you!

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Solutions to Our June Brain Teasers!

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Two weeks ago, we shared a pair of brain teasers sent in by a PuzzleNationer who discovered these particular deduction and math thinkers in a book of riddles and puzzles.

Today, we’re going to share not only the solutions, but how we got there! Please enjoy this brief solve and tutorial, courtesy of brain teasers from your fellow PuzzleNationers!

[Image courtesy of SharpBrains.com.]

Brain Teaser #1: There is a three-digit number. All three digits are different. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

Solution: 582

This is a fairly simple one, but if you’re unfamiliar with brain teasers, or uncomfortable in general with number puzzles, it can be off-putting. No worries, though! We’ve got you covered.

We know the second digit is four times as big as the third. That leaves only two options for those digits: 4 and 1 or 8 and 2.

If the first digit is three less than the second digit, it can’t be 4 and 1, because that would be 4 minus 1, or 1 for the first digit, and the first and third digits can’t be the same.

That means it’s 8 and 2 for the second and third digits. So if the first digit is three less than the second, the first digit is 5, and the three-digit number is 582.

calendar pages

Brain Teaser #2: When asked about his birthday, a man said, “The day before yesterday, I was only 25, and next year I will turn 28.” This is true only one day in a year – what day was he born?

Solution: He was born on December 31st and spoke about it on January 1st.

The wording in this one is especially important, because at first glance, this sounds impossible.

“Next year, I will turn 28.”

But if you look at the key word in what the man says — “turn” — the puzzle starts to unravel.

If next year, he will turn 28, this means that, at some point this year, he will turn 27. Which means he is currently 26.

Let’s look at what we know:

  • Day before yesterday: 25
  • Currently: 26
  • This year (at some point): 27
  • Next year: 28

Since he’ll be both 26 and 27 this year, the day before yesterday had to be last year.

Which means that yesterday was his birthday.

But at some point this year, he turns 27. That means both yesterday and the day before yesterday had to be last year.

Which leaves us with this timetable:

  • December 30 (day before yesterday, last year): 25
  • December 31 (yesterday, last year, his birthday): 26
  • January 1 (today, this year): 26
  • December 31 (later this year): 27
  • December 31 (next year): 28

He was born on December 31st and spoke about it on January 1st.

Did you unravel one or both of these brain teasers? Let us know in the comments section below! We’d love to hear from you.

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A Pair of Brain Teasers From Your Fellow PuzzleNationers!

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We love brain teasers here at PuzzleNation Blog. Whether they’re riddles, logic problems, math puzzles, or challenging bits of wordplay, we take on all comers here.

We’ve solved some doozies in the past, like the Brooklyn Nine-Nine seesaw brain teaser, the diabolical long division brain teaser, and the curious way to tell time brain teaser.

In April 2019, we did a whole week of brain teasers while your friendly neighborhood blogger was at a convention. Last year, we honored the life of mathematician and puzzle icon John Horton Conway by sharing two of his favorite brain teasers.

There’s a long, proud PuzzleNation Blog tradition of cracking whatever brain teasers come our way, whether we find them ourselves, stumble across them in pop culture, or receive them from our marvelous PuzzleNationers when asked for solving assistance.

A friend of the blog discovered two brain teasers in a book of riddles and puzzles during a bookshelf cleanout recently, and they sent them our way to share with you!

We’ll post them below, and share the solutions next week! Good luck, fellow puzzlers!

Brain Teaser #1: There is a three digit number. All three digits are different. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

Brain Teaser #2: When asked about his birthday, a man said, “The day before yesterday, I was only 25, and next year I will turn 28.” This is true only one day in a year – what day was he born?

Have you unraveled either of these brain teasers? Let us know in the comments section below! We’d love to hear from you.

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