Brain Teasers

[★ Blocks]

One is the correct answer. That's a very intuitive way to think about it. I think I remember that now from when I originally heard this. The way I did it was less elegant, by writing out an equation of motion and integrating velocity to get the path length. Interestingly, the beetles spiral an infinite number of times around the origin, but with finite path length one.

 

Brain's too good. Need to find harder problems. I heard a bunch of these (one a week) a few years ago, but I have a hard time remembering most of them in full.

[rootbear75]

Some Very Peculiar Sequences

 

Examine carefully the following sequences of numbers:

 

1

11

21

1211

111221

312211

13112221

1113213211

31131211131221

13211311123113112211

...

 

Although the sequences appear to behave totally at random, in fact, after the first sequence, each sequence is constructed in a precise and methodical way based on the previous one.

 

What is the next sequence?

 

BONUS: What is the sequence after that?

 

_______________________________________________________________________________

 

Strange Multiplication

 

In the multiplication shown below, the digits have been replaced by letters: different letters represent different digits. The same letters represent the same digits.

 

ABCDE
x   4
-----
EDCBA

 

What was the original multiplication?

Edited October 25, 2009 by rootbear75

[Dr Brain]

Strange Multiplication

 

In the multiplication shown below, the digits have been replaced by letters: different letters represent different digits. The same letters represent the same digits.

 

ABCDE
x   4
-----
EDCBA

 

What was the original multiplication?

21978
x   4
-----
87912

[p man]

Some Very Peculiar Sequences

 

Examine carefully the following sequences of numbers:

 

1

11

21

1211

111221

312211

13112221

1113213211

31131211131221

13211311123113112211

...

 

Although the sequences appear to behave totally at random, in fact, after the first sequence, each sequence is constructed in a precise and methodical way based on the previous one.

 

What is the next sequence?

 

BONUS: What is the sequence after that?

 

_______________________________________________________________________________

11131221133112132113212221

3113112221232112111312211312113211

[rootbear75]

Brain good job.

And p man good job as well.

 

Explanation of the sequence problem:

Starting with the second sequence. each sequence is simply a detailed description of the previous one. So, for example, the second sequence describes the first one: "one one;" that is, 1, 1. The third sequence describes the second: two ones; or 2, 1. The fourth describes the third: one two, one one; or 1, 2, 1, 1. The sequences in turn is described as follows: one one, one two, two ones (1 1 1 2 2 1). The sequence that follows is therefore 312211 since it describes the exact composition of the preceding sequence.

All of the above means that, in the series of sequences give, the next sequence is 111312211331121232112221. And then 3113112221232112111312211312113211.

 

______________________________________________________________________________________________--

An Incomplete Multiplication (solved)

 

Which digits must replace the question marks in the following multiplication in order for the result to be correct?

 

  126
x  ??
-----
  ???
????
-----
1?2?6

 

________________________________________________________________________________________________

The Football Fans

 

Thirty (30) fans hire a bus to attend a football game. On the way to the stadium they realize that exactly half of them are fans of one team and the other half are fans of the other team. With still some way to go before reaching the stadium, the bus develops mechanical problems and the driver announces to his passengers that the only way to continue the journey is for half of them to get out and walk.There is a huge fight that doesn't stop until the driver speaks to them again and suggests a way of selecting the passengers who are to get off the bus.

"All of you," he said, "get into a big circle. When you are ready, beginning at this spot, I'll count nine people clockwise. The ninth person leaves the circle and continues on foot. And so forth until fifteen people have left the circle."

 

Suppose that you are one of the fans. How should you arrange all of the other fans of your team so that none of them will have to walk? (You are Team A , the other fans are Team B )

Edited October 26, 2009 by rootbear75

[★ Lynx]

http://www.wired.com/gaming/virtualworlds/magazine/17-05/puzzle_answerkey

[Chambahs]

+1 for the ruin win!

[🜲 Samapico]

An Incomplete Multiplication

 

Which digits must replace the question marks in the following multiplication in order for the result to be correct?

 

  126
x  ??
-----
  ???
????
-----
1?2?6

 

126 x 81 = 10206

 

(who cares about the numbers to add in the middle of there)

Just tried it iteratively... multiplier had to be at least 80 to result in a 10000+ number, and less than 99 to be 2 digits...

 

 

The Football Fans

(You are Team A , the other fans are Team B )[/b]

AAABB BBABA BAAAA BBBAA BBBAB ABABA

[rootbear75]

An Incomplete Multiplication

 

Which digits must replace the question marks in the following multiplication in order for the result to be correct?

 

  126
x  ??
-----
  ???
????
-----
1?2?6

 

126 x 81 = 10206

 

(who cares about the numbers to add in the middle of there)

Just tried it iteratively... multiplier had to be at least 80 to result in a 10000+ number, and less than 99 to be 2 digits...

I need all of the numbers

 

and you are wrong on the football one

 

______________________________________________________________-

A School in Babel

An international school has 250 students, each of whom speaks several languages. For any pair of students, say A and B, there is one language that A speaks that B doesn't and another language that B speaks but A doesn't.

 

What is the minimum number of different languages spoken in the school?

Edited October 26, 2009 by rootbear75

[Chambahs]

Why would you need all the numbers? he simply just skipped the adding part, you can fill in the blanks.

[rootbear75]

Why would you need all the numbers? he simply just skipped the adding part, you can fill in the blanks.

because im going by a book.

the book wants the numbers, if it didnt want the numbers, it wouldnt have put in the blanks

Edited October 26, 2009 by rootbear75

[🜲 Samapico]

First row is 126x1 = 126

other row is 126x8 = 1008

 

See how useless that was?

[Chambahs]

Its an optical illusion to make you think its harder than it really is, when sama figured it out ez pz by not letting the ?'s effect his way of thinking the simplified way.

[rootbear75]

Fine w/e... sama you got that one...

 

anyways these two still havent been solved:

 

The Football Fans (solved)

 

Thirty (30) fans hire a bus to attend a football game. On the way to the stadium they realize that exactly half of them are fans of one team and the other half are fans of the other team. With still some way to go before reaching the stadium, the bus develops mechanical problems and the driver announces to his passengers that the only way to continue the journey is for half of them to get out and walk.There is a huge fight that doesn't stop until the driver speaks to them again and suggests a way of selecting the passengers who are to get off the bus.

"All of you," he said, "get into a big circle. When you are ready, beginning at this spot, I'll count nine people clockwise. The ninth person leaves the circle and continues on foot. And so forth until fifteen people have left the circle."

 

Suppose that you are one of the fans. How should you arrange all of the other fans of your team so that none of them will have to walk? (You are Team A , the other fans are Team B )

 

___________________________________________________________________

A School in Babel

An international school has 250 students, each of whom speaks several languages. For any pair of students, say A and B, there is one language that A speaks that B doesn't and another language that B speaks but A doesn't.

 

What is the minimum number of different languages spoken in the school?

Edited October 26, 2009 by rootbear75

[Chambahs]

A, A, A, A, B, B, B, B, B, A, A, B, A, A, A, B, A, B, B, A, A, B, B, B, A, B, B, A, A, B

[rootbear75]

+1 cham

[🜲 Samapico]

The school in babel... that would be 251

Each has its own language, and add 1 common language to fit the 'several languages' requirement.

[rootbear75]

nope...

 

What is the MINIMUM number of languages spoken

Edited October 27, 2009 by rootbear75

[🜲 Samapico]

250 then

[Chambahs]

2

 

Or no wait. 1 is the minimum.

[rootbear75]

An international school has 250 students, each of whom speaks several languages. For any pair of students, say A and B, there is one language that A speaks that B doesn't and another language that B speaks but A doesn't.

 

What is the minimum number of different languages spoken in the school?

[★ Lynx]

125

[🜲 Samapico]

By 'any pair of students' , you mean any pair at any given time, or you make pairs first, then you give them languages?

 

Cause... if you pair them as you want, 3 languages would be enough, but if the condition has to be true for any pair you might choose, I do believe you'd need 250

[rootbear75]

No...

(i'll post the answer and explanation in about an hour or so if you still cant get it)

[rootbear75]

The minimum number of languages spoken in the school is 10.

Suppose that the set of languages spoken in the school {I₁, I₂, I₃,..., I₉, I₁₀}. Using the elements of this set, 252 five-element sets can be formed. These 252 sets have the characteristic that if we take any two of them, each will contain one element that the other does not contain. If we take 250 of these sets of languages, and assume that they are, in some order, the languages spoken by the school's 250 students, it can be observed that given any two of these students, A and B, there is a language spoken by A and not spoken by B, and another language spoken by B and not spoken by A. This means that it is possible that only 10 different languages are spoken in the school.

In order to prove that it could not have been 9 (or fewer) languages spoken in the school, it is necessary to show thatout of the 512 subsets of a set of 9 elements, once can't find 250 that satisfy the conditions of the problem.