Cognitive Reflection Test and Puzzle Thread

Mental Calculation, Mathematics, and Puzzles
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Have you ever heard of the Cognitive Reflection Test?

It is only three questions, but apparently, most people miss them.

Here they are, if you want to give it a try.

1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

  1. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

  2. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

One website says that Only 48 percent of MIT students sampled were able to answer all the questions correctly." Maybe MIT students are just in a hurry, because the questions are easy if you just stop for a moment to think.

Here’s a better puzzle:

What is the next item in this sequence?
1, 11, 21, 1211, 111221, 312211, 13112221, …

If you know any good puzzles, post them below. It would be interesting to see some more puzzles that rely on knowledge of memory techniques to solve…

Warning – spoilers will be in the comments below. :slight_smile:

1 Like
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  1. $0.05
  2. 500 min? (if 5 machines 5 min 5 widgets, 1 machine 25 min 5 widgets, 1 machine 5 min 1 widget, 100 machine 500 min 100 widgets)
  3. HAH! 47.

Now, that of course depends how long of a time period they had to answer them. Also, you basically told us they were tricky, prepping us to doubt basic assumptions.

For that number thing, I’ll guess something like 423443? Or perhaps 4111222211?

Bateman

Moar puzzles please.

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Number one and number three are correct. For number two, calculate how long it would take one machine to make one widget. The answer is in your parentheses there. :slight_smile:

1 machine 5 min 1 widget
5 machines 5 min 5 widgets
100 machines ? minutes 100 widgets…

I didn’t figure out the last one without checking the answer. I like that puzzle, because it involves alternate ways of looking at numbers. Try saying the numbers out loud.

There is a second part to that last puzzle, which is: how long does it take until you see the first 4 appear?

If anyone has good puzzles, post them below. I will search around for some more tonight.

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Of course, 5 minutes. Used a faulty mental shortcut. (If 1 takes 5 min, then 100 take 500!).

The numbers: 1, 11, 21, 1211, 111221, 312211, 13112221, …
If there is a ‘11’, it turns into a 2. If there’s a 2, it stays. If there’s a 111, it turns into a 3. Ones split into two ones if they’re alone, and there’s a 1 added to the beginning and the end each ‘turn’.

So, using that, still not really ‘getting’ the puzzle, After 13112221, it would be 11132222111. Unless 2’s do something when there’s more than one of them(perhaps 4 of them turn into a 4?), but I doubt it. The 4’s could never appear using the statements above, so I’m either missing something or they never appear.

Bateman

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Yes – fours never appear. :slight_smile:

The next item in the sequence is: 1113213211, but it can go on indefinitely.

Another hint: “one one, two one, one two one one, …”

I didn’t get that one without looking it up.

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SPOILERS, DON’T READ IF YOU LIKE MATH CHALLENGES

Ah, but that would be easy.

One one, two one, one two one one…

1, 11, 21, 1211, 111221, 312211, 13112221,
11132222111
1113213211

So, when 1’s move on(?) to a 2 or a 3, they leave behind, on the right side of that number, another 1. Because they divided before ‘moving on’. Or it could be when those 3 2’s turned into a 3, leaving a 1 on the left of it.

So for the number of the digit to increase, there has to be more of them than the digits value. (3’s need 4 3’s next to one another to move to a 4).

After 1113213211 it’s 3132113221? And then 13113223311? (Would prefer a yes/no answer)

I can’t figure out what this has to do with speaking the numbers(yet). Also, I keep thinking of binary for some reason, even though this is at least tertiary.

Ok. Got it. 1, 11, 21, 1211. One One(11) = 1, Two One(21) = 11, One Two One One(1211) = 21, and then One One One Two Two One 111221= 1211. Basically, One One means there’s only One ‘1’. This builds the next number, 11 = One One.

So after 1113213211 (Three One One Three One Two One One One Three One Two Two One) it’s 31131211131221.

Good puzzle.

Bateman

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Yes, that’s it. :slight_smile:

I like that tricky mental shift between homophonic adjectives and nouns.

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SPOILERS AGAIN

How much fun I would have missed…

There can never be a 4 because there can never be 4 of the same number in a row. There can’t be One One One One, because 11 would be two one. There can’t be a Two one, one one, one two, since the first and the middle would combine to three one.

I do like that shift as well. One one, two one… Wait a minute… One ONE! Perhaps that’s why I kept thinking binary. They always come in pairs, adjective-noun.

Bateman

Can’t really think of any math puzzles. Perhaps someone else could chime in? Kinma?

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I saw this question on LinkedIn. I clicked through several pages of those almost-10,000 answers, and most are wrong. :slight_smile:

( 1+1+1+1+1+1+1+1+1+1+1+1\times0+1=? )

(The original question was missing two addition signs.)
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Looks very easy.

For some reason, people feel compelled to add all the 1’s together before multiplying.

DoNe.

Bateman

11

Correct. :slight_smile:

It was interesting, because some people were very confident about their incorrect answers.

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Here’s another sequence puzzle that might amuse mnemonists.

What is the next number?

(1,20,33,400,505,660,777,… )

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Pretty neat.

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Spoilers, don’t read below if you don’t want to.
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1,20,33,400,505,660,777,…
It looks to me a lot like a simple binary system- 1, 10, 11, 100, 101, 110, 111, and now 1000. This would be 8000.
Edit: And I see how it makes sense. Each number uses the number it is in the '1’s place. 10 is 2 in binary, so 20. 11 is 3, so 33.

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you guys know who martin gardner is?
here’s a puzzle by him
idkPuzzle 1. Twelve pentominoes are arranged in a 6x10 rectangle as is shown in the topmost diagram. Can you divide the rectangle, along the black lines only, into two parts that can be fitted together again to make the three-holed rectangle shown in the bottom diagram?

Puzzle 2. Arrange the twelve pentominoes to form a 6x10 rectangle but in such a way that each pentomino touches the border of the rectangle. Of the several thousand fundamentally different ways of making the 6x10 rectangle (rotations and reflections are not considered different), only two are known to meet the condition of this problem. Asymmetrical pieces may be flipped over.

I have a book of puzzles by him based on russian folktales I like to do every now and then
original url

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I didnt format it correctly so I posted the source link

edit I also challenge everyone to do it visually and without paper

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The 1, 2 & 3 questions are very easy to me
Learn lateral thinking by Edward De Bono, he shows how to twists problem sideways.

The math erhm… I mean I encountered some of these from IQ tests, although i didn’t take the math thing here, on the IQ tests I solved 4 out of 5 correctly, I don’t know if it’s the same thing and I don’t want to look at it right now. Oh yeah 140 IQ :stuck_out_tongue: but I feel like thinking at a new angle is much wise than thinking intelligently, though.