## July 3rd, 2015 New York Times Puzzle

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KnightExemplar
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### July 3rd, 2015 New York Times Puzzle

www.nytimes.com/interactive/2015/07/03/ ... lving.html

I'll not say much about the puzzle outside of spoiler text.

Spoiler:
I was pretty close to stating "Numbers double" as the sequence. But then I decided to test other sequences and managed to learn that it was simply "numbers that increase from left to right". I guess this is more of a psychology puzzle as opposed to a math puzzle. So... I'm not sure if its good karma to be posting it here. Nonetheless, it does provide an "overly" simple puzzle. I hope yall enjoy.
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Vytron
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### Re: July 3rd, 2015 New York Times Puzzle

For those too lazy to click (it took a long while to load)

A short game sheds light on government policy, corporate America and why no one likes to be wrong.
Here’s how it works:

We’ve chosen a rule that some sequences of three numbers obey — and some do not. Your job is to guess what the rule is.

We’ll start by telling you that the sequence 2, 4, 8 obeys the rule:

[2] [4] [8] Obeys the rule

Now it’s your turn. Enter a number sequence in the boxes below, and we’ll tell you whether it satisfies the rule or not. You can test as many sequences as you want.

[ ] [ ] [ ] [Check]

Commentary
Spoiler:
The thing doesn't actually allow me to send numbers, but I suspect this is the "Black Swan" puzzle:

The idea here is that you have some premise like:

All swans are white

And now, you start testing for white swans, and every time you find another you're like "there we go! This gets me closer to proving there's no swans of another color!" While actually it's a waste of time, because no matter how many ones you test, once you find a black swan you'll be wrong.

In this case, people have their premise (what's the rule) and attempt to prove it by sending things that fit that rule. But are always told that whatever they send fits the rule, but that the rule they're thinking of it's not the right one.

What's wrong? They should be testing for stuff that does NOT fit their rule! The black swan.

The problem people have is that they've seen an example of increasing numbers, and so, they keep trying to send series of numbers that increase, but THAT's the rule!

So, whenever they try something that doesn't follow that rule (say, send 8, 4, 2 - the black swan) they got it.

And the lesson is to look for counterexamples instead of looking for things that prove your premise is right, which is useless.
Last edited by Vytron on Thu Jul 02, 2015 11:54 pm UTC, edited 2 times in total.

Deva
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
Started with doubling too. Assumed a somewhat tricky problem. Seemed too easy. Tried to break it, consequently. Ended 8 Yes / 5 No (some unnecessary).
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measure
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### Re: July 3rd, 2015 New York Times Puzzle

I solved it after this sequence of guesses:
Spoiler:

Code: Select all

`   1,    1,    1  No.   0,    0,    0  No.   0,    1,    2  Yes!   0,    9,   23  Yes!  87,    1,   -4  No.  88,   89,   83  No.   0,    1,    3  Yes!   0,    1,    4  Yes!   0,    1,   25  Yes!  25,   26,   12  No.   2,    1,    0  No.   2,    0,    1  No.  89,  223, 2945  Yes!`

SPACKlick
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
Tried 8 4 2 No! So order matters
Tried 73 75 79 Yes! Gap ratio doesn't matter
Tried 1, 1, 2 No! Doubles don't work
Tried 1, 4, 2 No! All must ascend
Tested ascending Correct.

Not sure I ruled everything out before guessing but meh

I prefer a different puzzle that tests the same thing.

Spoiler:
4 cards are on the table showing

2 A 7 D

You are told the cards follow the rule "All D's have a 7 on the back" which cards do you turn over to see if it's true?

Sizik
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### Re: July 3rd, 2015 New York Times Puzzle

Veritasium did a video featuring the same puzzle as the OP.

SPACKlick wrote:I prefer a different puzzle that tests the same thing.

Spoiler:
4 cards are on the table showing

2 A 7 D

You are told the cards follow the rule "All D's have a 7 on the back" which cards do you turn over to see if it's true?

Spoiler:
2, A, and D, to check that the D has a 7 on the back, and that the 2 and A don't have a D.
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SirGabriel
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
Am I the only one who thought to test non-integer values? I would have tested irrational, imaginary, and complex values too, but it only accepts numeric inputs.

Vytron
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
@SirGabriel: That would be a great lateral thinking puzzle.

And thus this game was born.

brenok
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### Re: July 3rd, 2015 New York Times Puzzle

I had seen the puzzle both in the Veritasium video mentioned and on the Harry Potter and the Methods of Rationality fanfiction.

The idea also reminds me of the game called Zendo, although it involves geometric shapes and allows multiple guesses.

SteelCamel
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
No, I tried both negative and fractional numbers. Despite what it said, I got quite a few "no" answers as it seemed too simple and I was looking for a trick that wasn't there. I started off with the obvious choice of doubling:

1 2 4 Yes
500 1000 2000 Yes
0 0 0 No

so not multiplication, and addition seems to have already been ruled out. So it could be simply order:

2 4 6 Yes
2 1000 50000 Yes
0 1 2 Yes
8 4 2 No

So it looks like it's order that matters. But this is where I think it's too simple... Have I missed something? Wait, I don't know that all three numbers have to be in order:

2 1000 5 No
1000 5 6 No
1 2 2 No
1 2 3 Yes

Hmm, looks like it is order of all three numbers... I still think that's too simple - this is going to "shed light on government policy, corporate America and why no one likes to be wrong", after all - so lets throw a few things at it and check:

-4 0 4 Yes
-50000 -2 -1 Yes
1.5 2 2.001 Yes

Looks pretty clear then. I spent a few minutes thinking about it, couldn't think of anything else it could be, and submitted "The numbers must be in ascending order" - while wondering what deep philosophical insight I'd missed, and was surprised to find it correct.

Who
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
I'm not sure if I would have gotten it if it hadn't been for the fact that "0 0 0" and "-1 -2 -4" don't increase.

I started by trying "16 32 64" and "128 256 512", to see if sequential powers of 2 would continue to work, and they did. (I was kinda thinking of it as a "what is the next number in this series" problem, and expecting "plot twist, it's a simple quadratic series".)

Then I tried "0 0 0", and found that it did not work. I tried "3 6 12" to see if it was only powers of 2, but that worked.
Then I decided to try and see what would happen with things other than positive integers. "-1 -2 -4" didn't work, but "1 2 4" (Tried because the negatives didn't work) did.
.5, 1, 2 also worked, proving that it was fine with fractions.
At this point I was kinda confused and thinking of "doubling but only if it increases" but decided that that was a weird rule and probably wasn't the case.
I tried 10, 20, 40 for no reason at all.
I tried 10, 20, 30 to see if it wasn't doubling. And that was about when I won. I tried a bunch more to see if it was something a bit stronger than just "increasing" (By coming up with random increasing numbers which seemed arbitrary) and also tested "1 2 2" to see if that worked, though looking back on it I should have tested every combination of increasing/decreasing/staying equal after figuring out it was probably something to do with increasing. It could have been "the 3rd must be bigger than the 2nd" and I would have been wrong. (Though looking at the puzzle from a meta level, "increasing" was more likely than "the 3rd must be bigger than the 2nd", because increasing is really simple and basic and easy to understand and even though "3rd>2nd" is a weaker rule, "increasing" already makes the point that you need to check for weaker rules and also has the advantage of being so simple and only one word that whoever fails to guess it will feel really really dumb.

Actually I think I still would have gotten it had they limited me to positive integers, but I'm not sure. I probably would have been paranoid about not getting a single no. But most of the math I've done where I've checked numbers, I wasn't trying to make a rule as strong as it could be, I was just checking that the rule I had applied and then I would try to prove it once I'd checked that it usually applied. Saying "All sequences of doubling positive integers fit the rule" would not have been wrong, even if it wouldn't have been as complete as it could have.

Vytron
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### Re: July 3rd, 2015 New York Times Puzzle

Spoiler:
SteelCamel wrote:No, I tried both negative and fractional numbers. Despite what it said, I got quite a few "no" answers as it seemed too simple

It's because most people keep trying ascending numbers and getting yes'. It's when you insert something like 0 0 0 that you're doing it right, and then it becomes simple, but thinking about 0 0 0 (or numbers not ascending) is the hard part for most people (in one of the videos brenok linked to it can be seen that if you try this with random people in the street most will give up.)

Ralp
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### Re: July 3rd, 2015 New York Times Puzzle

What I find most interesting is the way that the free-form responses are parsed to guess whether your answer is right or wrong:
Spoiler:

Code: Select all

`        var probablyWrong = ["doubl", "expon", "multipl", "^", "**", "power", "two", "2", "twice", "as big", "nth", "rais"];        if (hasAny(probablyWrong, sentence)) {            return false;        }        // if you have the right words, and no buts.        var seemsRight = ["larger", "increas", "greater", "small", "less", "big", ">", "<", "go up", "ascending"],            weaselWords = ['but ', 'not ', 'odd'];        if (hasAny(seemsRight, sentence) & !hasAny(weaselWords, sentence)) {            return true;        }            return false;`

taemyr
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### Re: July 3rd, 2015 New York Times Puzzle

Vytron wrote:
Spoiler:
SteelCamel wrote:No, I tried both negative and fractional numbers. Despite what it said, I got quite a few "no" answers as it seemed too simple

It's because most people keep trying ascending numbers and getting yes'. It's when you insert something like 0 0 0 that you're doing it right, and then it becomes simple, but thinking about 0 0 0 (or numbers not ascending) is the hard part for most people (in one of the videos brenok linked to it can be seen that if you try this with random people in the street most will give up.)

Actually 0 0 0 is a bad example here. Because the puzzle is intended to show your tendency towards confirmation bias having uninteded no's is a problem. The issue is that people tend to not try sequences that don't obey the rule they think of. The hard part is to think to try something like 1,2,3 - ie. something that does not follow the "every number is double the previous". (In other words if I designed this puzzle I would require only positive numbers).

Vytron
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### Re: July 3rd, 2015 New York Times Puzzle

It's a puzzle about thinking outside the box, and three 0s is thinking outside the box, so it's not worse than three 1s, and restricting to positive numbers feels artificial.