Tag Archives: deduction

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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[Image courtesy of SharpBrains.com.]

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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PN Product Review: ThinkFun’s Cold Case: A Pinch of Murder

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pinch of murder box

[Note: I received a free copy of this game in exchange for a fair, unbiased review. Due diligence, full disclosure, and all that.]

A puzzle can leave you baffled for the longest time. You think you’ve examined it from every possible angle, and yet, you’re still left without a solution. Then a fresh pair of eyes arrives, and suddenly all of the pieces fall into place.

Maybe it’s a friend or colleague who sees something you’ve missed, or simply hasn’t been stuck running through the same paths over and over. Or maybe it’s you, having taken a break from the puzzle, stepped away, and returned, now recharged and refreshed and ready to start again.

And that’s the mindset behind ThinkFun’s new Cold Case series. In this puzzle game, you are picking up where a previous investigation left off, trying to close an unsolved murder case.

pinch of murder 2

In today’s spoiler-free review, we’re looking at A Pinch of Murder, the second of two Cold Case mysteries being released in the next few weeks.

A Pinch of Murder presents players with the story of Harold Green, a loyal churchgoer found dead late one afternoon in 1983.

You have transcripts of police interviews with suspects, witness statements, evidence, photographs, and other items collected by the police during their initial investigation. But it’s up to you to comb through the evidence and find what they missed.

There is so much material here that it’s a bit daunting at first. The dizzying array of suspects and names takes a while to get a handle on, even as you carefully read through every scrap of evidence. The presentation is very impressive, with different types of paper and full-color reproductions of photographs and other materials really adding to the immersive feel of the game.

And this case file feels totally different from the one included in the previous entry in the Cold Case series, A Story to Die For. You receive bits of evidence in unfamiliar formats, the interviews are presented differently, and it genuinely feels like a separate team of investigators put this set together.

pinch of murder 1

Harold Green’s life unfolds before you in little bits and bobs, and the glimpses you get of his town, the people around him, and his day-to-day existence feel so credible.

And once you think you’ve cracked the case and found answers for all of the questions left behind by the initial investigation, you can test your theory by going to the ThinkFun Cold Case website and submitting your answers.

If you’re on the wrong track, the replies from the website will give you clues on where to look in order to correctly solve the case. And if your detective skills are in tiptop condition, you’ll get more information and a chance to read the suspect’s confession!

But with no shortage of suspects and a wealth of material to pore over in order to track down the killer and tie up every loose end, this is hardly a cakewalk. You’ll need to pay attention, read between the lines, and make connections like a proper detective.

Solving puzzles is great fun, but to actually feel like you’re solving a murder? That’s something special. Whether you’re solving alone or with friends, the hour or two you spend eliminating suspects and narrowing down the truth in this mystery game will absolutely be worthwhile. When you have that a-ha moment and you know you’ve earned it, there’s nothing quite like it.

ThinkFun has only made two of these so far, and I cannot wait to get my hands on the next ones.

[Cold Case: A Pinch of Murder is part of ThinkFun’s Cold Case series, designed for players ages 14 and up, and is available for $14.99 from ThinkFun and other associated retailers. Pre-orders start June 1st! Links coming soon!]

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Solution to our May the 4th Jedi Logic Puzzle!

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Last week, we celebrated Star Wars Day (aka May the Fourth) with a Jedi-themed brain teaser for our fellow puzzlers and PuzzleNationers to solve!

How do you crack this Star Wars-inspired Jedi mystery? Let’s find out together!

On a small planet in the Mid Rim, a group of Jedi defeated several squads of battle droids. Reporters had a hard time piecing together descriptions of the five Jedi who saved the day, even after interviewing many witnesses.

The only thing the reporters were sure of? The names of the five Jedi:

  • Drosco Wrs
  • Ko Duus
  • Pramyt Gorc
  • Wendo Grars
  • Seredwok

Each of the Jedi wielded a different color lightsaber (green, yellow, blue, orange, or purple). Each held a different title within the Jedi Order (Padawan, Knight, Master, Instructor, or Council Member). And each of them was a different species (Barabel, Bith, Nautolan, Twi’lek, or Wookiee).

Based on the information gathered below, can you figure out which lightsaber color, title, and species belongs with which Jedi?

1. Drosco Wrs (whose lightsaber is either orange or green) is neither the padawan nor the knight.

2. Either Ko Duus or the Bith is the council member, and the other has the yellow lightsaber.

3. The Jedi with the blue lightsaber (who isn’t on the council) is either the Twi’lek or the Wookiee; if Twi’lek, then Drosco Wrs is the instructor, but if Wookiee, then Seredwok is the instructor.

4. The padawan (who has neither the blue lightsaber nor the green lightsaber) is not Seredwok.

5. Wendo Grars (who isn’t the knight) doesn’t have the yellow lightsaber or the blue lightsaber.

6. The Barabel (who is either Pramyt or Seredwok) isn’t the Jedi with the purple lightsaber.

7. The master has either the purple lightsaber or the yellow lightsaber. Neither the purple lightsaber nor the yellow lightsaber are wielded by the Nautolan.

So, where do we begin?

Well, there’s a lot of information here about the lightsabers, and that’s where we can start.

We know that the Nautolan doesn’t have the purple or yellow lightsabers (rule 7) or the blue lightsaber (rule 3). Similarly, we know that the Barabel doesn’t have the purple lightsaber (rule 6) or the blue lightsaber (rule 3). But we can also deduce that it doesn’t have the yellow lightsaber, because either Ko Duus or the Bith have the yellow lightsaber (rule 2), and Ko Duus isn’t a Barabel (rule 6).

That means the green and orange lightsabers are split between the Nautolan and the Barabel. That also means that Drosco Wrs is either the Nautolan or the Barabel, because his lightsaber is either green or orange (rule 1). But since he can’t be the Barabel (rule 6), Drosco Wrs is the Nautolan.

Let’s start our chart there:

sw puz 1

But we know more about Drosco Wrs. He is neither the padawan nor the knight (rule 1) and according to his lightsaber color, he is not the master (rule 7). He is also not the council member, who must be the Bith or Ko Duus (rule 2), so he is the instructor.

Because he is the instructor, we now also know that the Twi’lek has the blue lightsaber (rule 3).

We also know that the Jedi with the blue lightsaber isn’t the padawan (rule 4), the master (rule 7), the council member (rule 4), or the instructor (since Drosco Wrs is the instructor and his lightsaber is either green or orange). That means that the blue lightsaber is with a Twi’lek who is a knight.

Let’s update our chart:

sw puz 2

If we return to the Barabel, according to our chart they’re not the knight or the instructor, and they can’t be the master based on their possible lightsaber color. So they’re either the padawan or the council member. But the council member is either Ko Duus or the Bith (rule 2), and Ko Duus can’t be a Barabel (rule 6). So the Barabel must be the padawan.

And since Seredwok isn’t the padawan (rule 4), Pramyt Groc is the Barabel and the padawan.

But that’s not all. We know that the Barabel’s lightsaber is either green or orange, and the padawan’s lightsaber can’t be green (rule 4), so we have our first complete row.

sw puz 3

It’s taken a lot of work to get here, but now things are rolling.

Drosco Wrs, our Nautolan instructor, could only have a green or orange lightsaber (rule 1), and since orange is the padawan’s color, we now know his lightsaber is green.

So green, blue, and orange are all accounted for, and the council member cannot have a yellow lightsaber (rule 2), so the council member has a purple lightsaber, and the master has a yellow lightsaber.

Wendo Grars can’t have orange, blue, or green, based on our chart, nor can she have yellow (rule 5), so she has the purple lightsaber, making her the council member.

Our chart is looking pretty full now:

sw puz 4

Since Wendo Grars is the council member, Ko Duus must be the wielder of the yellow lightsaber (rule 2), which also makes Wendo Grars the Bith.

And process of elimination gives us one name left — Seredwok — and one species left — Wookiee — to assign.

So our completed chart looks like this:

sw puz 5

Oh, we also hid a little puzzly easter egg in this puzzle. Each of our Jedi names were anagrams of popular puzzles:

  • Drosco Wrs = Crossword
  • Ko Duus = Sudoku
  • Pramyt Gorc = Cryptogram
  • Wendo Grars = Rows Garden
  • Seredwok = Word Seek

Did you manage to unravel this devious Jedi-themed logic puzzle? Did you spot the wordplay in the Jedi names? Let us know in the comments section below! We’d love to hear from you.

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