Mr. Martin And The Mismanaged Airport Terminal

Question

There is a small international airport in Greece. It has just 6 gates, lined up from 1 to 6 going away from the front desk. Tickets here only have the last names of passengers and gate numbers clearly read, while the rest of the information is on QR codes. Due to an issue with their electronic billboards, the airport staff have placed signs that say “Destination [Country Name]” at each gate in the primary language of that country.

Today six men who all happen to have the last name of Martin, were late for their flights. As the men rush past the front desk, they all collide, dropping their tickets. Each man frantically picks up a ticket, sees his last name on it, and runs to the gate on the ticket. The front desk worker speaks all six languages fluently, and could have easily helped them all, but each man thinks they have the correct ticket. The men will only go to the front desk if they are aware that the gate printed on the ticket they have is not the destination they wish to go to. All six men are aware of how the airport is handling the electronic billboard issue.

Can you match each man to his intended destination, the ticket he picked up, and his mother tongue and second language?

Clues

1. Each man speaks exactly two languages, and no two men speak exactly the same two languages. Each language is completely unrecognizable to the four men who don't speak it. Every man was born in, and has lived his whole life in, one of the six countries and his mother tongue is primarily spoken in that country (i.e. Zulu in South Africa and Spanish in Spain).

2. Of the men who were planning to go to South Africa, Ireland, and the Netherlands, two were going home, while the third eventually missed his plane. Of the two men who missed their flights, they had enough time to swap tickets and make their flights.

3. The 6 people are: The man who picked up the ticket to Poland, The man who is going to Poland, The two men who can speak Polish, The only man who can speak to both of the men who speak Polish, and Connor.

4. Between the man who was born in Poland and Kellan, one was going to the Czech Republic, while the one who learned Dutch at 15 years old was the one who picked up the Czech Republic ticket. After the accident, both of these men ran past gate 3, but neither of them could read the sign there for the Irish flight. Bernard never went to the gate for the Czech Republic plane, but if he had he would have known the planes destination but would not have been able to tell the man who picked up the Czech Republic ticket what it was.

5. The man who went to gate 6 was the first person to realize he was at the wrong gate, was the only person to realize that he had picked up the wrong ticket on his own, and was the only person who checked each of the gates as he ran back to the front desk for help. Fortunately, after checking at least one other incorrect gate, he recognized the gate with the sign in Dutch, which was his correct gate.

6. From the time that all six men had made it to the gates printed on the ticket they had picked up, to when all six planes had left the airport, a total of three ticket swaps were made. The first two involved the men who could speak Zulu and Lars, in some combination. The third involved the man who had picked up the ticket to Spain and one of the men who spoke Dutch.

7. The swap that involved the man who wanted to go to Spain and the man from the Czech Republic was the only one where the two men were unable to communicate. Instead, the front desk worker, who had been made aware of the situation, called the stewardess at Gate 2 and explained the situation. She swapped the tickets of the two men at her gate. No man ever gave away his correct ticket.

8. A man who could speak Spanish was the only person who picked up the correct ticket. He knew that he had picked up the correct ticket when he reached his gate. From the time that the other five men had made it to their incorrect gates to when the last of the six planes departed, there were exactly four times where one of the other five men ran past this man's gate, although not necessarily the same person. James was the only other person who never left his gate.

The puzzle is solvable using the above clues, however I added these last five clues to make things easier. I'd encourage you to try solving it without them.

The only man to pick up the correct ticket was going to Ireland.

The man who went to gate six first was not the man born in South Africa.

The second swap was at gate five.

Lars learned Polish when he was 11.

A man who is at the wrong gate will only be unaware of that fact if he doesn't expect to understand the sign of his intended destination and he doesn't understand the sign at the gate he is at.

These last hints I'm adding because I feel like maybe anyone who might be working on it still is stuck. So this is kind of an order of events for the most difficult part of the puzzle.

Start by figuring out as much information about clue 8 that you can. Focus on the Original Destination - Ticket Picked Up box.

Use Clue 8 and the counting of four people to figure out where the first swap must have happened.

Last, use the box below the logic grid to figure out what must be true about who was the first to swap. It was either Lars, Mother Tongue Zulu, or Second Language Zulu. Two of those set as the person who went to Gate 6 will create contradictions. That will help you solve almost the whole thing.

I'd like your honest opinions about this puzzle. It is my first time writing my own logic grid puzzle. Did you solve it? How hard did you find it? What did you like about it? What could I have done better? Thanks.

Once anyone posts the correct answer, if they used some of my hints, I'll mark their answer as correct, but I'll post an answer using just the 8 clues.

Answer 1

Took me a while, but here's the solution:

Step by step:

(Note: I like full square grids for solving these riddles, helps me spot any squares I missed marking off. The information is the same as in a triangular one, just doubled along the main diagonal. I marked new entries in a different shade of red and green compared to the old ones, so it's easier to see what is new compared to the last step.)

First, this is the base grid: Only interesting thing here is that the first and second language obviously have to be different.


Next, include everything that is directly stated in the text. Clue 3 blocks everything Polish from another and from Connor.


Clue 4 tells us a few things:

• Kellan doesn't speak Polish as his first language
• The man destined for Czechia isn't the man who grabbed the Czech ticket
• The man who grabbed the Czech ticked speaks Dutch as his second language
• Neither of {Kellan; the man who speaks Polish as his first language; the man destined for Czechia; the man with the Czech ticket} speaks Irish at all
• As Bernard couldn't communicate with the man with the Czech ticket (who we know speaks Dutch), Bernard doesn't speak Dutch
• As Connor is neither a native Polish speaker (per clue 3) nor is he called Kellan, Connor is none of the people in clue 4, meaning he doesn't speak Dutch as a second language, didn't grab the Czech ticket, and didn't want to go to Czechia



Clue 5 doesn't give use any information that we can directly fill in, so will will get back to it later. Clue 6 tells us that Lars doesn't speak Zulu, as every language is only spoken by two people, and Lars is swapping tickets with both of them.

Before we come to clue 7, we should think about the whole swapping process. Swapping tickets only makes sense if one of the participants is aware that the other man has his ticket. We know that the man from clue 8 already has the correct ticket, so he won't swap with anyone. James also never swapped his ticket per clue 8. But since he didn't start with the correct ticket, this must mean that he was unaware that he had the wrong ticket and couldn't understand what was written on the gate he ended up (and he importantly didn't expect to, because otherwise, he would be suspicious that he couldn't read anything at his wrong gate, and search for his correct ticket). Otherwise, if you recieve a new ticket, you go to that gate. There were three swaps, and four people that moved around (everyone except the lucky guy from clue 8 and James).

We also know that only the guy who started at gate 6 noticed that his ticket was wrong (per clue 5). We also know that he went and found his Dutch flight, where he then swapped tickets with the man there. This man then checked out gate 6. He also realized that this isn't his flight (otherwise, there would be no more reason to keep swapping tickets), and went to the man on the desk (only the first guy actually checked the gates directly to look for his flight per clue 5!). The clerk told him the correct gate, where he swapped his ticket with the man there. This third man also checked out gate 6, realized it wasn't his, went to the clerk, found his correct gate and swapped his ticket there. This was the third swap. The last guy went to gate 6 as well, didn't find anything wrong with it and stayed there, breaking the chain of swaps.

Back to clue 7: We know that the last swap involved a man with a Spanish Ticket per clue 6. We also know that the one swap involved a man who wanted to go to Spain. These must refer to the same swap. Otherwise, the man travelling to Spain would already have his ticket from one of the previous swaps, and it wouldn't be passed around at the last swap. Remember, you don't swap tickets unless at least one person gets their correct one. Together with clue 6, this means:

• The man travelling to Spain knows Dutch (but we don't know whether as a first or second language)
• The man with the Spanish ticket has Czech as his first language
• The man travelling to Spain doesn't know any Czech

For the lucky man from clue 8, there are three options left for flights where the grabbed ticket was the correct one - Ireland, South Africa and the Netherlands. These are the same countries as in clue 2. As the lucky man was at the correct gate, he didn't miss his flight, and was therefore travelling home. This means that his second language is Spanish (as clue 8 says that he speaks Spanish) and his native language is the same as his flight and ticket. However:

• The man from clue 5 was looking for the Dutch flight. Therefore, the lucky man can't be on that flight as well.
• Both Zulu-speakers were involved in ticket swaps per clue 6. As only two men speak each language, the lucky man can't be from South Africa.
The lucky man is therefore from Ireland, travelling to Ireland with his correct Irish ticket, and he speaks Spanish as a second language.


We know that Mr. Lucky-Irish isn't called Lars (had to swap his ticket with the Zulu-Boys), James (missed his flight by standing around), Bernard (speaks Czech) or Kellan (Mr. Lucky-Irish neither went to Czechia, nor had he the ticket for it). We also know that since he speaks Irish and Spanish as first and second language, the reverse option is blocked for everyone, as no two men speak the same pair of languages.

We know that the guy who started at gate 6 (call him Gate-6-Guy) successfully found his Dutch gate. As he found it, he hasn't missed his flight. By clue 2, we can conclude that the guy flying to the Netherlands flew home, so Gate-6-Guy has Dutch as his first language. We also know from clues 6 and 7 that the other guy speaking Dutch wanted to go to Spain, so those are the two travel destinations of Dutch speakers. We also know that the guy who wanted to fly to South Africa missed his flight.

There need to be two people who missed their flights: James, and someone else who has James' ticket. The only person who could end up with the wrong ticket is the one who swapped theirs in the third swap, checked out gate 6 and found nothing wrong with it. This poor sod (I call him PoorSod) would be the Czech man who initially grabbed the Spanish Ticket. Regarding James: As he was stationary and didn't swap his ticket, he is

Not Gate-6-Guy

Not a zulu speaker

Not the Czech man who grabbed the Spanish ticket (who after all swapping has James' ticket)

Now we think about the gates, and figure out where the first swap between gate-6-guy and the other man he gave his ticket happened. We know that he started at gate 6 and went past at least one other gate until he found his flight, so that rules out gate 5 as well. Gate 3 is occupied by Mr. Lucky-Irish, and gate 2 is where the final swap happened, so it can't be the gate he was at as well. This leaves gate 1 and 4 as the only two options.
We also know that there were four instances of people running across gate 3 per clue 8. If gate-6-guy found his Dutch flight at gate 1, he would cross gate 3 once on his way there. The man he swapped his ticket with would then run to gate 6, find out he's wrong there and head all the way back to the clerk next to gate 1, resulting in two more runs across gate 3. He then goes to his correct gate for the second swap, and the only options for that are gates 4 or 5, bumping us up to four runs. But the next guy also goes to gate 6, heads back to the clerk, swaps his ticket at gate 2, with the person there also heading to gate 6, which adds up to two more runs. So gate 1 is out, and the Dutch flight is at gate 4.

Now, languages: We know that there are six languages, and we know per clue 3 that there are two polish speakers, and one person who can communicate with both of them. This is only possible if three people form a sort of language-triangle where they share three languages between them. X and Y speak Polish, X and Z speak common language A, Y and Z speak common language B. As this leaves three men out, they also must form such a language triangle.

We know that Lars is in the same language triangle as the Zulu-Speakers, as they could swap without language problems.

As PoorSod (the guy who missed his flight despite swapping at the 3rd swap) speaks Czech and couldn't communicate with Lars or the Zulu-Boys, he's not in their language triangle

Gate-6-Guy speaks Dutch, and was involved in the first swap. Therefore, Dutch is in the same triangle as Zulu.

As Mr. Lucky-Irish speaks both Irish and Spanish, these two must be in the same triangle. This must be different from the Zulu-Dutch-triangle, as there can't be four languages in the same one. Therefore, Irish, Spanish and Czech must form one triangle, and Dutch, Zulu and Polish the other one.
As Mr. Lucky-Irish speaks Irish as his first and Spanish as his second language, the other two pairings in that triangle are forced as well: One man speaks Spanish as his first and Czech as his second language, the other one Czech as his first and Irish as his second.

The plane at gate 6 was correctly identified as not their plane by all three men of the Zulu-Dutch-Polish-triangle, while PoorSod from the Czech-Irish-Spanish-triangle didn't understand the signs there. This plane can't be from Czechia, as PoorSod would've noticed that this is not his plane. It can't be from Ireland, as that plane is at gate 3, and it can't be from Spain, as that one is at gate 2, where the final swap happened. It can't be Dutch, that one is at gate 4, and it can't be from Poland, as the man who grabbed the Polish ticket can't be in the Polish language triangle per clue 3, but Gate-6-Guy, who grabbed the ticket for that flight, is in that one. This means that gate 6 has the South African flight. This means that Gate-6-Guy initially grabbed the SA-Ticket, and that James (who's the only other person stranded) actually wanted to go there.

We can also deduct a few more things based on the language pairings.

Lars speaks both Polish and Dutch, since he's the Non-Zulu-Speaker in the Zulu-triangle.

Bernard speaks Czech and is therefore unable to understand any language of the the Zulu-Dutch-Polish triangle.

Bernard never went to the Czech gate despite speaking Czech, so he didn't want to go to Czechia in the first place (otherwise, he would've known he's at the wrong gate). The only other option left is that he wanted to go to Poland.

The man who's a native Czech speaker also has Poland as the single travel destination option left. So Bernard is actually a native Czech speaker wanting to go to Poland. As we know that the native Czech speaker is PoorSod, aka the person who started out with the Spanish ticket and speaks Irish as a second language, Bernard is fully defined.

We know that James has to have Bernard's ticket to Poland, which means that James doesn't speak Polish himself, which also forces everything about him.

Connor, who is not in the Dutch-Zulu-Polish triangle, only has a single language option left, namely Irish as a first and Spanish as a second language. This also fully solves Connor, who is Mr. Lucky-Irish.

By everything we know, Lars could have grabbed one of three tickets, the South African, Czech or Dutch one.

NL: The Dutch ticket was the one Gate-6-Guy acquired at the first swap, so it wasn't picked up by the person who wanted to go to the Netherlands. But Lars knows Dutch, meaning that he would've noticed if he found himself at the wrong flight. As the person who was approached by Gate-6-Guy in the first swap didn't notice that he was at the wrong gate on their own, this one is out.

SA: This would mean Lars is Gate-6-Guy.

CZ: This would make Lars the man who was approached in the second swap, who actually wanted to go to Spain, and exchanged tickets with Bernard in the third swap. We know that Lars doesn't understand Zulu or Spanish, so Lars wouldn't have seen a difference between the two when he checked out gate 6, and wouldn't have made an additional swap. Therefore, this option is also false.
We can conclude that Lars is Gate-6-Guy who found out that he was at the wrong gate because the writing there didn't look Dutch to him.

After that, it's just a case of filling in the correct squares, everything is forced:


The six men are:

Kellan: From SA, also speaks Dutch, grabbed the Czech ticket and wanted to go to Spain, made his flight

Bernard: From Czechia, also speaks Irish, grabbed the Spanish ticket and wanted to go to Poland, missed his flight

Connor: From Ireland, also speaks Spanish, grabbed the Irish ticket and wanted to go to Ireland, made his flight

James: From Spain, also speaks Czech, grabbed the Polishticket and wanted to go to SA, missed his flight

Philip: From Poland, also speaks Zulu, grabbed the Dutch ticket and wanted to go to Czechia, made his flight

Lars: From the Netherlands, also speaks Polish, grabbed the SA ticket and wanted to go to the Netherlands, made his flight

As for feedback, I really enjoyed this riddle. The only thing I'd change is to make it a bit more clear how the swapping works. It says that people will go to the front desk if they notice that their ticket is wrong, but

Lars found the Dutch flight on his own, and I wasn't sure initially whether he would still go to the front desk or not. Same for the hint the stewardess swapped the tickets of two people at gate 2, it took me a second to understand how there are two men at the same gate. But apart from that, this is a really well crafted riddle

Answer 2

This is not an answer to the puzzle itself but instead a response to request for feedback. Please note that my feelings are quite subjective and are coming from someone who couldn’t finish the puzzle. Someone who was able to solve it might feel differently.

I thought this puzzle had great potential. I used to love these tick/cross logic puzzles when I was younger but soon found them repetitive and boring so any novel approach to the genre will always pique my interest. This puzzle certainly did that! I love the idea of clues referring to the languages people speak without knowing if it’s a mother tongue or second language - it requires a bit of extra thinking that many puzzles in this genre fail to achieve. I also like how you used aspects such as people being unable to communicate with each other and understand what’s written on their boarding pass.

The story itself is also well told and fun to read. A hilariously unlikely but still plausible situation will always draw the solver in!

Sadly I never got to the stage of really using any of the creative logic as I was unable to progress further than one tick and a lot of crosses. Essentially I felt that the clues were too hard and relied a lot on the solver being able to work out what the setter is thinking. The gate numbers I think are the main complication here. What does two people running past gate 3 tell me? How can two people both find themselves at gate 2? Is there a layout to the gates that would help me to solve the puzzle.

These puzzles ultimately sit in the realms of strict mathematical rigour and solvers are unlikely to make inferences unless they are 100% certain that they are correct - typically because either the preamble or the clues strictly lay out the inferences that can be made. For example, in your puzzle you refer to people travelling “home.” An Irish expat living in Poland might consider either (or both) Ireland or Poland “home.” I think I can guess what you mean here but I shouldn’t have to guess.

Another minor point is that the grammar in some clues doesn’t quite make sense. I’m pretty confident I know what you mean in clues 4 and 5 but I had to reword some of the sentences in my head to get there. These sorts of things are easily fixed.

Overall I think you have the skills to write really fun tick/cross logic puzzles! Perhaps exploring a similar idea with languages as this one or another novel twist on the genre with easier clues, more freebies and no “guess what I’m thinking” aspects will yield a really fun puzzle. I’d certainly be keen to tackle another one of your puzzles!

Answer 3

Here are the steps using just the 8 clues and none of the hints.

Step 1:

Get all of the obvious stuff out of the way. These mostly come from the fact that everything that has to do with Poland is unrelated. Connor has nothing to do with Poland also. The problem with Clue 3 is that there isn't an easy way to represent that on the grid. Thus the bottom box is better for representing it. It should look like this:

Step 2:

This involves Clue 8. Note that Clue 8 says that only one person picked up their correct ticket. This means that in the Original Destination - Ticket Picked Up box, there is just one correct answer in the TL-BR diagonal. So we go through each one. Clue 3 says that the Polish ticket was not picked up by the person going to Poland. Clue 4 says that the Czech Republic ticket was not picked up by the person going to the Czech Republic. Clue 5 says that the person going to the Netherlands found his gate, meaning he didn't pick up the correct ticket. Lastly, Clue 6 and 7 show that the person who picked up the ticket to Spain was involved in a swap, and that no man gave his correct ticket away. This leaves us with South Africa and Ireland. Clue 2 tells us that if we can prove that the person going to these three locations made it to their correct gate, that they are going home. Clue 1 tells us that "going home" means that they speak the mother tongue of that location. We know from Clue 6 that both of the Zulu speakers swapped their tickets. Thus they couldn't be the person to have picked up the correct ticket. So the person going to Ireland must be the native speaker of Ireland. Clue 8 also tells us that they speak the second language of Spanish. Along with the more obvious clues, this gives us with the following logic grid:

Step 3:

Now we know that Clue 8 is talking about the Gate to Ireland, which Clue 3 tells us is Gate 3. So, from this we can conclude that the person who went to gate 6 (Clue 5) was going to gate 4. This is because if we assume that gates 1 or 2 was the gate to the Netherlands, the count that Gate 3 would get is always greater than 4. This is because each man will go to gate 6 before going to the front desk for help. So, because Clue 5 says that he searched at least one other incorrect gate before finding the Netherlands gate, it must be gate 4.

Step 4:

Now ask why anyone would know they are at the wrong gate. There are 4 possibilities. 1. They expect to read the sign and they can. 2. They expect to read the sign and they can't. 3. They don't expect to read the sign and they can. And 4. They don't expect to read the sign and they can't. Only option 4 results in someone failing to realize that they are at the wrong gate. Clue 5 tells us that the man who went to gate 6 was the only person to realize he was at the wrong gate on his own. Since Clue 5 also tells us that he was going to the Netherlands and Clue 2 tells us that he was going home, and thus his Mother Tongue is Dutch (Clue 1), it means that he must be option 1 or 2. In order for there to be 3 total swaps, the next two men in the chain must also realize that gate 6 is incorrect. They must be option 3 since they were option 4 before. So p2 and p3 can speak the language at gate 6, thus p1 must be option 2 since they expected to read the sign in Dutch.

Step 5:

So, there are 3 people who passed gate 3 after the initial accident. These are MT Dutch, MT Polish, and SL Dutch (MT Dutch didnt pick up the ticket to CR because that person is SL Dutch. He also doesnt want to go to CR because he wants to go to the Netherlands, thus these are the 3 people). MT Dutch went to gate 6. The 3 people who could have gone to gate 6 are Lars, MT Zulu, and SL Zulu. It can't be MT Zulu for obvious reasons. Therefore it must be Lars or SL Zulu. Whoever it is, they are MT Dutch. When they go to gate 4, they must be able to communicate with TPU Netherlands. But because that person didn't know they were at the wrong gate, they must speak the Second Language of MT Dutch as their Mother Tongue. Therefore it is either MT Zulu (in the case that SL Zulu is MT Dutch), or it is SL Zulu's Mother Tongue (in the case that Lars is MT Dutch). Since we know that gate 4 is T Netherlands, the person at gate 4 must therefore be D Czech Republic. This leads us down a rabbit hole where we can deduce a ton of information from Clues 4, 5, 6, and 7. It is left as an exercise for the reader but the following table must be true. White cells have been deduced earlier or by the deductions made here. Green cells are deduced from Clue 1 and process of elimination. Blue cells are either South Africa or Poland (and their languages) with Yellow cells being the other. If Lars is G6 then Yellow is South Africa while Blue is Poland. If SL Zulu is G6 then Yellow is Poland while Blue is South Africa.

Step 6:

Now we have to fit these two tables together. Because I know the answer, let's fit SL Zulu in to G6 first. This means that he picked up the Polish ticket. It means that MT Zulu is SL Polish. It also means that G5 is MT Polish. This creates a contradiction. On our table created by Clue 3, the person who picked up the ticket to Poland is specifically not the only person who can speak to the two men who speak Polish. But if SL Zulu is G6, he must be both. Thus G6 is Lars and Yellow is South Africa. So, combining the colored table with our Table from Clue 3, this leaves us with the following table.

Step 7:

So, from Clue 4, we know that Bernard cannot communicate with the person who picked up the ticket to the Czech Republic (Kellan). We also know from Clue 4 that Bernard can speak Czech. That means Bernard either picked up the ticket to Poland or he was trying to go to Poland. We also know that James never left his gate. Since MT Polish was the second person involved in the ticket swap at gate 4 and gate 5, by process of elimination, that must be Philip.

Step 8:

So let's work through what happened. Lars goes to gate 6, he knows he should understand the sign, but he can't. He heads to the front desk, but sees the sign at gate 4. He swaps his ticket with Philip, using Polish. Philip then goes to gate 6 and reads the sign in Zulu. He goes to the front desk, who tells him to go to gate 5. Connor sees him pass by his gate twice, once to the front desk, and once on his way to gate 5. At gate 5, Philip and Kellan speak in Zulu. Kellan goes to gate 6, reads the sign, and goes to the front desk. Connor sees this. Kellan learns that he needs to go to gate 2 for Spain. Once there, he cannot communicate with that person. They swap tickets, with help from the gate stewardess, and that person goes to gate 6. He cannot speak Zulu and he doesn't expect to understand the sign, so he waits there. The only gate that was never visited was gate 1, which is where James is. This means that James picked up the ticket to Poland, and Bernard picked up the ticket to Spain. This leaves us with the following grid and table as our answer.

Congratulations to @PebNischl for figuring it out in a slightly different way than I did.