Answer to our Thanksgiving Logic Puzzle!

Last week, we celebrated Thanksgiving with a social distance-themed logic puzzle in honor of this time of year and the peculiar circumstances of 2020.

So let’s take a look at how to untangle this puzzle and sort things out so everyone enjoys the holiday, shall we?


First, a quick reminder about the puzzle, so the clues are fresh in our minds (and you have one last chance to solve it before we walk you through the solution).

On a curious Thanksgiving in 2020, five housemates were social distancing, each engaged in different activities throughout the day. (One was streaming Hulu.)

Each housemate (including Brian) wore a different outfit — one was wearing a tank top and shorts — and was doing their activity at a different time that day (1 PM, 2 PM, 2:30 PM, 3 PM, or 3:30 PM).

From the information provided, can you determine what time each housemate did which activity, as well as what outfit they were wearing?

1. The person doing Zoom trivia did so earlier than Alex but later than the one who wore a t-shirt and jeans.

2. Luke’s activity was earlier in the day than Denise’s, but later than that of the person who wore a Christmas sweater and pants.

3. Alex (who was wearing a Pokemon onesie) had her activity earlier than the person texting Grandma but later than Denise.

4. The person playing Among Us did so later than the person Facetiming their Mom, but earlier than the one wearing pajamas (who did their activity earlier than Adam).


Okay, first things first, let’s organize the information we have.

  • There are five housemates: Adam, Alex, Brian, Denise, Luke.
  • There are five activities: Facetiming Mom, playing Among Us, streaming Hulu, texting Grandma, doing Zoom trivia.
  • There are five outfits: Christmas sweater/pants, Pajamas, Pokemon onesie, Tanktop/shorts, T-shirt/jeans.

Since many of the clues reference who or what happened earlier or later than other events, it makes sense to use the times as our anchor points, so our starting grid should look like this:

turkey logic 1

And we can immediately mark down who did the activity at 1 PM. In clue 1, the person doing Zoom trivia did their activity earlier than Alex, so Alex wasn’t the person at 1 PM. Clue 2 tells us that both Luke and Denise had someone doing activities before them, so it couldn’t be them at 1 PM. And Clue 4 tells us that the person in pajamas did their activity before Adam, so he couldn’t be the 1 PM person either. That leaves Brian as the 1 PM person.

That information tells us more as well. Alex can’t be the 2 PM person, because Clue 1 says both the Zoom trivia person and the person in t-shirt and jeans did activities before Alex. Denise can’t be the 2 PM person, because Clue 2 says both Luke and the person in the Christmas sweater did activities before Denise. And Adam can’t be the 2 PM person because Clue 4 says that both the person playing Among Us and the person wearing pajamas did activities before Adam. So Luke must be the 2 PM person.

Not only that, but since Luke did his activity after the person in a Christmas sweater and pants, that makes the sweater/pants Brian’s outfit.

We can fill in one person based on time as well. Clue 3 tells us that Alex’s activity was after Denise’s, so Alex can’t be the 2:30 PM person. And Clue 4 tells us that Adam’s activity happened after the person Facetiming Mom, the person playing Among Us, and the person in their pajamas, so Adam can’t be the 2:30 PM person. That leaves Denise as the 2:30 PM person.

So now our chart looks like this:

turkey logic 2

Let’s look at the outfits now. We know from Clue 3 that Alex is wearing the Pokemon onesie, but we’re not sure where to place Alex yet. But we can place the pajamas based on what we know.

In Clue 4, we’re told that the person wearing pajamas has their activity after the person Facetiming Mom and the person playing Among Us, and before Adam. So Adam is out. Alex and Brian are also out, because we know what they’re wearing. And Luke can’t be the person in pajamas, because his activity is second (2 PM) and at least two activities have to be done before the person wearing pajamas. That leaves Denise as the person in pajamas.

That leaves only two outfits unaccounted for: the tanktop/shorts and the t-shirt/jeans. But we can eliminate those as well. In Clue 1 we’re told that the person in t-shirt and jeans does their activity before both the person doing Zoom trivia and Alex. But Adam can’t be that person, because Adam’s activity happens after the person Facetiming Mom, the person playing Among Us, and the person wearing PJs. So Adam is wearing a tanktop and shorts, and Luke is wearing a t-shirt and jeans.

Let’s look at our chart now:

turkey logic 3

As you can see, I’ve added notes below for person/outfit combos we know that we can’t yet place.

But the information above does tell us something else.

Clue 4 tells us that the person playing Among Us did so later than the person Facetiming Mom, but earlier than the person wearing pajamas. And we know the person wearing pajamas is Denise. So that means Luke is playing Among Us and Brian is Facetiming Mom.

This information also tells us what Alex is doing. Clue 1 tells us Alex is not doing Zoom trivia, and Clue 3 tells us that Alex is not texting Grandma. And since she can’t be playing Among Us or Facetiming Mom, the only remaining option is streaming Hulu.

This same process of elimination can tell us who did the last two activities. We know Denise isn’t playing Among Us, Facetiming Mom, or streaming Hulu. But Clue 3 tells us she wasn’t texting Grandma either, so she must have been doing Zoom trivia.

Which means Adam was the one texting Grandma.

And since Clue 3 tells us that Alex’s activity happened before the person texting Grandma, we can complete our grid:

turkey logic 4

How did you do? Did you manage to unravel this holiday puzzler? Let us know in the comments section below! We’d love to hear from you!


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A Puzzle for Thanksgiving!

Happy Thanksgiving, PuzzleNationers!

Today is a day for celebrating with family and friends (although that’s harder this year), and giving thanks for all the good things in our lives.

We here at PuzzleNation want to thank you, our fellow puzzlers and PuzzleNationers, because you help make PuzzleNation one of the greatest puzzle communities in the world.

And when it comes to saying thanks, a Thanksgiving puzzle seems like the perfect offering. So we’ve cooked up a little Thanksgiving logic puzzle for you to enjoy!

Can you unravel this holiday puzzler?


On a curious Thanksgiving in 2020, five housemates were social distancing, each engaged in different activities throughout the day. (One was streaming Hulu.)

Each housemate (including Brian) wore a different outfit — one was wearing a tank top and shorts — and was doing their activity at a different time that day (1 PM, 2 PM, 2:30 PM, 3 PM, or 3:30 PM).

From the information provided, can you determine what time each housemate did which activity, as well as what outfit they were wearing?

1. The person doing Zoom trivia did so earlier than Alex but later than the one who wore a t-shirt and jeans.

2. Luke’s activity was earlier in the day than Denise’s, but later than that of the person who wore a Christmas sweater and pants.

3. Alex (who was wearing a Pokemon onesie) had her activity earlier than the person texting Grandma but later than Denise.

4. The person playing Among Us did so later than the person Facetiming their Mom, but earlier than the one wearing pajamas (who did their activity earlier than Adam).


Did you unravel this holiday puzzler? Let us know in the comments section below! We’d love to hear from you!

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Two Brain Teasers, Courtesy of Conway

John_H_Conway_2005_(cropped)

Last week, we penned a post celebrating the life and puzzly legacy of mathematician John Horton Conway, and several of our fellow PuzzleNationers reached out with their own thoughts or questions about Conway.

One recurring subject was about his love of puzzles and what kind of puzzles he enjoyed solving. So, naturally, I went hunting for some of Conway’s favorite puzzles.

As it turns out, Alex Bellos of The Guardian had me covered. Alex has a recurring puzzle feature on The Guardian‘s website where brain teasers and other mental trickery awaits intrepid solvers.

Years ago, Alex had asked Conway for suggestions for his column, and Conway offered up two tricky puzzles.

And now, I happily share them with you.


#1: The Miracle Builders

I had a window in the north wall of my house. It was a perfect square, 1 meter wide and 1 meter high. But this window never let in enough light. So I hired this firm, the Miracle Builders, who performed the impossible. They remodeled the window so it let in more light. When when they’d finished the window was a perfect square, 1 meter high and 1 meter wide.

How did they do it?


#2: The Ten Divisibilities

I have a ten digit number, abcdefghij. Each of the digits is different.

The following is also true:

  • a is divisible by 1
  • ab is divisible by 2
  • abc is divisible by 3
  • abcd is divisible by 4
  • abcde is divisible by 5
  • abcdef is divisible by 6
  • abcdefg is divisible by 7
  • abcdefgh is divisible by 8
  • abcdefghi is divisible by 9
  • abcdefghij is divisible by 10

What’s my number?

[To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…]


Did you solve one or both of these fiendish mind ticklers? Let us know in the comments section below! We’d love to hear from you.

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Answers to our Thanksgiving Logic Puzzle!

It’s been a week since Thanksgiving, so it’s about time we gave you the answer to our Turkey Day logic puzzle!

In case you missed it, here’s the puzzle:

Connor, Emma, Russell, and Taylor are celebrating Thanksgiving together. To save money, each of them is bringing a different side dish (cranberry sauce, green beans, mashed potatoes, or yams). Each of them is also bringing a different dessert (apple pie, chocolate cream pie, pumpkin pie, or sugar cookies). With the help of the clues below, can you puzzle out who brought which side dish and which dessert?

1. Emma didn’t bring the green beans, but she did bring pumpkin pie.
2. Connor brought the cranberry sauce, but he didn’t bring chocolate cream pie or apple pie.
3. The person who brought the yams also brought the chocolate cream pie.
4. Taylor brought the green beans.


Okay, last chance to solve it before we give you the solution!

Here we go!


Now, this isn’t as difficult as some of the diabolical brain teasers we’ve tackled in the past, but for someone new to logic puzzles and deduction, a puzzle like this can be daunting.

The key to logic puzzles is to organize your information in a simple and efficient way, so that you maximize the amount of information you glean from each clue.

So let’s list out our four holiday guests and all of the possible food options.

Now, let’s proceed through the clues and fill in our chart.

1. Emma didn’t bring the green beans, but she did bring pumpkin pie.

Since we know nobody brought the same dessert as Emma, we can black out pumpkin pie for everyone else, as well as blacking out the other dessert options for Emma, since each person only brought one dessert.

2. Connor brought the cranberry sauce, but he didn’t bring chocolate cream pie or apple pie.

When you add Connor’s info to Emma’s, you not only get his side dish and his dessert, since he didn’t bring chocolate cream pie, apple pie, or Emma’s pumpkin pie.

3. The person who brought the yams also brought the chocolate cream pie.

At first, this clue doesn’t seem to tell us much, because we don’t know who brought the yams or the chocolate cream pie. But we do know that Emma didn’t bring the chocolate cream pie, so she didn’t bring the yams either.

And if she didn’t bring the yams, the green beans, or Connor’s cranberry sauce, by process of elimination, she brought the mashed potatoes.

4. Taylor brought the green beans.

This last clue ties it all together. If Taylor brought the green beans, then Russell had to bring the yams. And since the person who brought the yams brought the chocolate cream pie, we know that was Russell as well, and Taylor brought the apple pie by default.

And there you have it. All that info in four simple clues.

We hope you enjoyed our little Thanksgiving logic puzzler!


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The Diabolical Long Division Brain Teaser!

From time to time, I’ll receive an email with a brain teaser I’ve never seen before. Sometimes they come from friends, or fellow puzzlers. Other times, PuzzleNationers will ask for my assistance in solving a puzzle that has flummoxed them.

That was the case with today’s puzzle, and I’ll admit, this one was a bit of a doozy to unravel.

longdiv1

Yup, an entire long division problem with only a single digit set. No letters or encryption to let us know which digits were repeated, as there are in Word Math puzzles published by our friends at Penny Dell Puzzles.

Just a 7 and a bunch of asterisks. “Is this doable?” the sender asked.

Yes, this is entirely doable, friend. Let’s break it down step by step.

First, we need to know our terminology. The 8-digit number being divided is our dividend. The 3-digit number we’re dividing into it is the divisor. The 5-digit number on top is our quotient.

For the other lines, let’s label them A through G for ease of reference later.

longdiv2

There we go. Now, where do we go from here? We start with what we know.

We know that 7 is the second digit in our quotient.

So our divisor, times 7, equals the number on line C. That’s a 3-digit number, which means the first number in our divisor is 1. Why? Because if it was 2, 2 times 7 would give us 14, which would be a 4-digit number on that line.

longdiv3

That means the quotient is somewhere between 100 and 142. (Why 142? Easy. I divided 1000 by 7, and 142 is the last 3-digit number you can multiply 7 against and still end up with a 3-digit answer for line C. 143 times 7 is 1001, which is too high.)

What else do we know from the puzzle as it stands?

Well, look at lines E and F. We bring both of the last two digits in the dividend down for the final part of the equation. What does that mean?

Remember how long division works. You multiply the divisor by whatever number gets you closest to the given digits of the dividend, subtract the remainder, bring down the next digit from the dividend, and do it all over again until you get your answer.

You multiply the first digit of the quotient times the divisor to get the number on line A. You multiply 7 times the divisor to get the number on line C. You multiply the third digit of the quotient times the divisor to get the number on line E.

Following this route, you would multiply the fourth digit of the quotient against the divisor to get the number on line G. But bringing just one digit down didn’t give us a number high enough to be divided into. Instead of needing more lines (H and I, in this case), we bring the last digit of the dividend down and press onward.

That means the fourth digit of the quotient is 0, because the divisor went into the dividend zero times at that point.

longdiv4

And there’s more we can glean just from the asterisks and what we already know. We know that every one of those 4-digit numbers in the equation begin with the number 1.

How do we know that? Easy. That first number in the divisor. With a 1 there, even if the divisor is 199 and we multiply it times 9, the highest possible answer for any of those 4-digit numbers is 1791.

So let’s fill those numbers in as well:

longdiv5

Now look at lines D, E, and F. There’s nothing below the 1 on line D. The only way that can happen is if the second digit in line D is smaller than the first digit on line E. And on line F, you can see that those first two columns in lines D and E equal zero, since there’s nothing on line F until we hit that third column of digits.

That means the second digit on line D is either a 0 or a 1, and the first digit on line E is a 9. It’s the only way to end up with a blank space there on line F.

longdiv6

I realize there are a lot of asterisks left, but we’re actually very close to knowing our entire quotient by now.

Look at what we know. 7 times the divisor gives us a 3-digit answer on line C. We don’t yet know if that’s the same 3-digit answer on line E, but since it’s being divided into a 4-digit number on line E and only a 3-digit number on line C, that means the third digit in our quotient is either equal to or greater than 7. So, it’s 7 or 8.

Why not 9? Because of the 4-digit answers on lines A and G. Those would have to be higher than the multiplier for lines C and E because they result in 4-digit answers, not 3. So the digit in the first and fifth places in the quotient are higher than the digit in the third. So, if the third digit in the quotient is 7 or 8, the first and fifth are either 8 or 9.

So how do we know whether 7 or 8 is the third digit in the quotient?

Well, if it’s 7, then lines C and E would have the same 3-digit answer, both beginning with 9. But line C cannot have an answer beginning with 9, because line B is also 3 digits. The highest value the first digit in line B could have is 9, and 9 minus 9 is zero. But the number on line D begins with 1, ruling out the idea that the numbers on lines C and E are the same.

That makes the third digit in the quotient 8, and the first and fifth digits in the quotient 9.

longdiv7

We know our quotient now, 97809. What about our divisor?

Well, remember before when we narrowed it down to somewhere between 100 and 142? That’s going to come in handy now.

On line F, we know those first two digits are going to be 141 or below, because whatever our divisor is, it was larger than those three digits. That’s how we ended up with a 0 in our quotient.

So, the number on line D minus the number on line E equals 14 or below. So we need a 900-something number that, when added to a number that’s 14 or below, equals 1000 or more. That gives us a field from 986 to 999.

And that number between 986 and 999 has to be divisible by 8 for our quotient to work. And the only number in that field that fits the bill is 992. 992 divided by 8 gives us 124, which is our divisor.

longdiv8

From that point on, we can fill out the rest of the equation, including our lengthy dividend, 12128316.

longdiv9

And there you have it. With some math skills, some deduction, and some crafty puzzling, we’ve slain yet another brain teaser. Nice work everyone!

[After solving the puzzle, I did a little research, and apparently this one has been making the rounds after being featured in FiveThirtyEight’s recurring Riddler feature, so here’s a link.]


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