Favorite Brain Teasers

I bet that every person on this board enjoys a good brain teaser. This thread is a place to share your personal favorite(s). That one special puzzle that drove you crazy years ago that you still remember today.
Anybody can post a puzzle, and there’s no reason why more than one cannot be working at the same time. The originator should post the answer if nobody gets it within a reasonable period-a couple or three days, generally. If you think you have the answer, you may prefer to send a pm rather than an open post, to give others a chance to continue working on it.
I’ll start:

I have a 10-volume hardback Battlestar Galactica anthology collection on my bookshelf. Each volume is exactly the same size: the pages total one inch in thickness, and each cover, front and back, is one eighth of an inch thick.
One night a tiny bookworm began boring into the bottom of the front cover of Volume 1. She bored straight up a short distance, then turned and bored a horizontal tunnel all the way into Volume Two, all the way through Volume Two, all the way into and through the back cover of Volume Three, at which point she turned downward, went out the bottom of the Volume Three back cover, and crawled off to eat somebody else’s books.
What was the length of the horizontal tunnel that she bored? (Go ahead and count the entire thickness of each cover that she ate through.)

[unowhoandwhy]

The answer is Q...

Nope, that doesn't sound right. Is it 1,987,654,321 miles?

Ummm...there's a reason I only took the minimum required math courses in high school, but I can't seem to remember what that reason was...

...oh wait, I remember now! I stink at word problems!

Naw, try again, Uno! The math part is real easy, on purpose. But visualizing the problem. . .now, that's another story entirely.
Clue: how observant are you?

[Dawg]

12.25 inches. Minus her body width, of course.

Total pages = 10 inches. Plus total cover thickness 2.5 inches. Minus the first and last cover, .25 inches.

Right?



I am
Dawg

[Rowan]

are the books sitting on the shelf in numerical order?
if they aren't there is no way to tell how many books she bored through before exiting through number 3.

[Dawg]

OK, I wasn't paying attention.

3 inches of pages plus .5 inches of cover. 3.5 inches.

Sheesh. I need to read through things more than once......

I am
Dawg

Originally Posted by Dawg

12.25 inches. Minus her body width, of course.

Total pages = 10 inches. Plus total cover thickness 2.5 inches. Minus the first and last cover, .25 inches.

Right?



I am
Dawg

Uh, nope. Re-read the question!

Originally Posted by Rowan

are the books sitting on the shelf in numerical order?
if they aren't there is no way to tell how many books she bored through before exiting through number 3.

Yes, the books are arranged properly.

[unowhoandwhy]

3/4 of an inch?

[bsg1fan1975]

2/3 of an inch? Uno, just like you I took the minimum reuqired math classes. I stink at math

Originally Posted by Dawg

OK, I wasn't paying attention.

3 inches of pages plus .5 inches of cover. 3.5 inches.

Sheesh. I need to read through things more than once......

I am
Dawg

Very sensible, very accurate arithmetically, and very wrong. Why?
['nother clue: go look at a bookshelf. Stare at the books very carefully (especially if you have a set of three or more books anywhere on the shelf), and then see if the answer doesn't slowly work its way into your brain.]

[Rowan]

Ack!! she'd be entering the back cover of book 3 and exiting through the front cover, because when we place a group of books on a shelf that are in a series we place them from right to left on a shelf.

Originally Posted by Rowan

Ack!! she'd be entering the back cover of book 3 and exiting through the front cover, because when we place a group of books on a shelf that are in a series we place them from right to left on a shelf.

Rowan,
I'll help you out. You're on the right track. But look again. They are still arranged left to right not right to left.
Laura

[Rowan]

ok I ment in relationship to each other sorry, ie the back of book one is up against the side of the bookshelf, the front cover is touching the back cover of book 2, and the front cover of book 2 is touching the back cover of book 3

[Dawg]

I figured it out. Books from left to right, right? Vol1Vol2Vol3, not Vol3Vol2Vol1, right?

1 3/8 inches. This assume she actually did not bore through the front cover of Volume 1. (if she did it would be 1.5 inches).

Am I right?

Of course, if the books were in upside down......

I am
Dawg

[BST]

What was the length of the horizontal tunnel that she bored? (Go ahead and count the entire thickness of each cover that she ate through.)

1 and 1/4 inches


1/8" each for front and back covers of Volume 2 + thickness of volume 2.
(the bookworm did not eat "through" front cover of Volume 1 or back cover of Volume 3 and never touched the pages of either Volume 1 or 3)

[Dawg]

She ate through the back cover of #3, BST.

1-3/8.

I am
Dawg

[amberstar]

My brain isn't working.........I'm not good at word problems either.

How far up did she go? Looking at my hard cover books I see that the pages are not even with the covers, they are set up higher than the bottom of the cover.
So........depending on how far up she bore she may have missed the pages of the books alltogether and just eaten the covers.

[BST]

Originally Posted by Dawg

She ate through the back cover of #3, BST.

1-3/8.

I am
Dawg

Hmm, ok.

But, I'm confused how she ate through the back cover and then, came out the BOTTOM of the back cover. That's why I didn't think she ate all the way through the back cover of Volume 3.

[Rowan]

Originally Posted by BST

Hmm, ok.

But, I'm confused how she ate through the back cover and then, came out the BOTTOM of the back cover. That's why I didn't think she ate all the way through the back cover of Volume 3.

but that would be the same then for the cover of volume 1 as well

"began boring into the bottom of the front cover of Volume 1."

[BST]

Originally Posted by Rowan

but that would be the same then for the cover of volume 1 as well

"began boring into the bottom of the front cover of Volume 1."

Right. That's why I thought the bookworm only went completely through 2 covers - the front and back of Volume 2.

OK, you have essentially the right answer. The covers of Volume 1 and Volume 3 are intended to be included "(Go ahead and count the entire thickness of each cover that she ate through."), so the correct answer is supposed to be 1 1/2 inches. Boring up through the front cover is just how she got to the starting point; the main idea is to note the way that a book sits on the shelf when its spine is facing outward. The bookworm never touches the pages of Volume 1 or Volume 3.

Next brain teaser, somebody?

OK, slow week at the bizarre bazaar, so I'll play again.

Ever notice that brain teasers are usually word problems, never math exercises? Seems unfair, since there are lots of people who don't hate math at all. Anyway, here's a math puzzle. This one kept me awake for a couple of hours on I-70 through southern Illinois, a tremendously flat and boring stretch of four-lane highway that kept insisting that I go to sleep on it. I didn't figure it out then, and later I gave up and started asking math experts for the answer, and nobody knew, so I finally had to work it out myself.

When I was much younger, I used to take "The Twelve Days of Christmas" literally. I figured that my true love ended up giving me 12 partridge-filled trees (one each day for 12 days), 22 turtledoves (two a day for 11 days) and so on. Final tally: 364 items. Question: what is the general formula for this kind of series, of any length? The pattern is (1) + (2+1) + (3+2+1) . . . and x is the number of entries. [Has anybody ever seen this series described in a math text? I haven't.]

[BST]

Originally Posted by Bombadil

This one kept me awake for a couple of hours on I-70 through southern Illinois, a tremendously flat and boring stretch of four-lane highway that kept insisting that I go to sleep on it.

Been on that stretch of I-70, YAWN, I agree with you. Many, many cornfields and overall beautiful landscape but, also very "hypnotic" on a driver.

Originally Posted by Bombadil

The pattern is (1) + (2+1) + (3+2+1) . . . and x is the number of entries.

The only mathematic operation that I can think of, at this early hour, is a factorial BUT, that isn't it because a factorial (x!) is a multiplication operation, i.e. -- 5! = 5*4*3*2*1 = 120. Maybe a "cousin" to this.

[BST]

Hey Bomb,

I did find some interesting information at the following site:

https://mathworld.wolfram.com/topics/Sequences.html

I haven't gone through all of them, though.

(I found this site by doing a Google search on 'Factorial'.)

BST

Originally Posted by BST

Hey Bomb,

I did find some interesting information at the following site:

https://mathworld.wolfram.com/topics/Sequences.html

BST

I looked at the page, and it may be there, but I would have to know what it is called. I just call it "The Twelve Days Formula" but I didn't see that listed, so they must call it something else.

[unowhoandwhy]

Do you want it expressed mathematically or as a total number of gifts?

Mathematically I would go with (12*1)+(11*2)+(10*3)+(9*4)+(8*5)+(7*6)+(6*7)+(5*8)+(4*9)+(3*10)+(2*11)+(1*12)=

As a total, it would be 364 gifts.

But, if you want to get fancy, the following website has some lovely solutions:

https://www.mcglaun.com/math/HOW%20MANY%20GIFTS.doc

Very interesting reading. But I worked out a formula that is even simpler:

((x+1)^3)/6 - (x+1)/6

Try it. It works every time!

[BST]

Very interesting reading. But I worked out a formula that is even simpler:

((x+1)^3)/6 - (x+1)/6

Try it. It works every time!

...and x = what??

Is this for the "12-day formula" ?

Originally Posted by BST

...and x = what??

Is this for the "12-day formula" ?

Right. In this case, x = 12. Total gifts after 10 days would be x = 10. And so on.