Game Post your Puzzles / Brain Teasers

[RobbieGray17]

Thought I'd start a puzzle thread, puzzles can be enjoying.

Try to refrain from cheating, its not in the spirit of the game, and its better to work it out yourself.

The first puzzle (from a past exam paper)

1. There are two cities, X and Y on opposite sides of a lake. A boat leaves X heading for Y at the same time a boat leaves Y heading for X. They travel at constant but different speeds. The boats pass each other 500m from X. After reaching their destinations they turn around and head back to their original cities at the same speed. They pass each other again 300m from Y. How wide is the lake between X and Y?

When I found the answer to this, I didn't exactly use a formula, I drew the problem out on paper, and used a rather crude method of calculating the distance.

2. There are 4 cities. A, B, C and D. The cities are arranged in a square, 1Km apart. If you have to connect all the cities together with roads. What is the minimum amount of road required to connect the cities. Remember the most obvious solution may not be the best one. This one requires some optimization.

And if you can, show your working out.

Post new puzzles when we finish the last ones. and have fun.

 

[CLFC23x]

these are actually hardish

 

[Quivorir]

Thought I'd start a puzzle thread, puzzles can be enjoying.

Try to refrain from cheating, its not in the spirit of the game, and its better to work it out yourself.

The first puzzle (from a past exam paper)

1. There are two cities, X and Y on opposite sides of a lake. A boat leaves X heading for Y at the same time a boat leaves Y heading for X. They travel at constant but different speeds. The boats pass each other 500m from X. After reaching their destinations they turn around and head back to their original cities at the same speed. They pass each other again 300m from Y. How wide is the lake between X and Y?

When I found the answer to this, I didn't exactly use a formula, I drew the problem out on paper, and used a rather crude method of calculating the distance.

2. There are 4 cities. A, B, C and D. The cities are arranged in a square, 1Km apart. If you have to connect all the cities together with roads. What is the minimum amount of road required to connect the cities. Remember the most obvious solution may not be the best one. This one requires some optimization.

And if you can, show your working out.

Post new puzzles when we finish the last ones. and have fun.

Without putting too much thought into it would the answer be 3? The roads in an 'N' shape. Or does each city need to be connected to each?

 

[RobbieGray17]

Without putting too much thought into it would the answer be 3? The roads in an 'N' shape. Or does each city need to be connected to each?

Well 2 sqrt 2 would be more optimized, 2.82. but thats still not the answer.

 

[TassieEagle]

Well if the Cities don't all need to be connected to each other then the simplest i can see is just an "X" shape so it would be 2km? Or just build a 1km wide, 1km long road, thus turning everything inside the square of the cities into a gian parking lot

As for the first one I can't think of the algebra needed but x-500 y-300 or similar would make an appearance.

 

[RobbieGray17]

Well if the Cities don't all need to be connected to each other then the simplest i can see is just an "X" shape so it would be 2km? Or just build a 1km wide, 1km long road, thus turning everything inside the square of the cities into a gian parking lot

As for the first one I can't think of the algebra needed but x-500 y-300 or similar would make an appearance.

LOL! the idea is to minimize cost as well as travel times.

The X is 2 sqrt 2. which is 2.82KM

the angle is pi/4 = (sqrt2) *2

 

[BigEasyPeasy]

Hey guys, just had a look at these...

1. Applying equations to describe the motion/ paths of the two boats and then using cross multiplication tells me the width of the lake is 1200m across.

2. This one is trickier; I used Steiner points to work out the shortest possible path. I'll do my best to draw it:

A B


P1 P2


C D


Join the dots from P1 to P2- and thus connect this line segment to the corners. Apply appropriate trig equations with some simplifying and the result is 1 + SQRT3. Or in other words about 2.732...

 

[BigEasyPeasy]

Gahhh, formatting hates me. Those letters are supposed to be in a large square, with a small line between the P1 and P2.

 

[RobbieGray17]

Hey guys, just had a look at these...

1. Applying equations to describe the motion/ paths of the two boats and then using cross multiplication tells me the width of the lake is 1200m across.

2. This one is trickier; I used Steiner points to work out the shortest possible path. I'll do my best to draw it:

A B


P1 P2


C D


Join the dots from P1 to P2- and thus connect this line segment to the corners. Apply appropriate trig equations with some simplifying and the result is 1 + SQRT3. Or in other words about 2.732...

Sounds right for the second one, theres a video explanation on youtube explaining it. With the first problem, if I remember correctly, I set the distance to zero when the boats crossed paths.

 

[Druitt Soldier]

Don't read the post below unless you want to know the answer...

Heres one I stumbled across a couple of months ago that I thought was pretty good.

There are four men buried in the sand in a straight line up to their head. There is a wall separating one of them from the other three and every man is wearing a hat. Two men are wearing a white hat and two are wearing a black hat. Each man doesn't know what colour hat they are wearing and they can't turn their head to see what hat every other man is wearing. They can only see the hat of the guys in front of them.

Another man is standing over them with a gun and says that one of them must tell them what colour hat he is wearing or he will shoot them all. If someone makes a wrong guess then the gunman will kill also kill him. One of the buried man shouts out the colour of his hat with total confidence and is correct. So they all get to live.

Which man knew what colour his hat was?

Clues
- The man don't know what order they are in, only that there are two black hats and two white hats.
- No one can see over the wall.
- The man at the back can see both people in front of him but not the man on the other side of the wall.

I'll make a diagram so you can see how the men were all positioned in the sand.

| = wall

B = man with black hat

W = man with white hat

> = direction he is facing


B> | <W <B <W

 

[danger_to_walker]

Heres one I stumbled across a couple of months ago that I thought was pretty good.

There are four men buried in the sand in a straight line up to their head. There is a wall separating one of them from the other three and every man is wearing a hat. Two men are wearing a white hat and two are wearing a black hat. Each man doesn't know what colour hat they are wearing and they can't turn their head to see what hat every other man is wearing. They can only see the hat of the guys in front of them.

Another man is standing over them with a gun and says that one of them must tell them what colour hat he is wearing or he will shoot them all. If someone makes a wrong guess then the gunman will kill also kill him. One of the buried man shouts out the colour of his hat with total confidence and is correct. So they all get to live.

Which man knew what colour his hat was?

Clues
- The man don't know what order they are in, only that there are two black hats and two white hats.
- No one can see over the wall.
- The man at the back can see both people in front of him but not the man on the other side of the wall.

I'll make a diagram so you can see how the men were all positioned in the sand.

| = wall

B = man with black hat

W = man with white hat

> = direction he is facing


B> | <W <B <W

If the man at the back can see the two in front of him, and they are both wearing the same colour hat, then he knows that he is wearing the opposite colour.

If both in front of him are wearing different coloured hats, however, he cannot say anything. The second in line can then deduce from his silence, that he and the man at the front are wearing different coloured hats. Therefore, he is wearing the opposite colour of the person in front of him.

 

[Druitt Soldier]

If the man at the back can see the two in front of him, and they are both wearing the same colour hat, then he knows that he is wearing the opposite colour.

If both in front of him are wearing different coloured hats, however, he cannot say anything. The second in line can then deduce from his silence, that he and the man at the front are wearing different coloured hats. Therefore, he is wearing the opposite colour of the person in front of him.

Correct.

Very nicely done.

 

[kickazz]

OK this is an oldie, most probably are, but here goes:


BT, Richo, Rompingwins and Bruce are walking to the G when they come across a rickety old bridge that they need to cross over.

The bridge can only carry two people at a time, and it is also very dark and they have with them one torch. If more that two go on the bridge at once it collapses and they fall into the Yarra. Likewise, if they try to cross the bridge without the torch they will also likely fall as the bridge is very old and has holes and s**t.

They all walk at different speeds, such that if each were to cross alone, it would take them this amount of time respectively:

Bruce 1 minute
Richo 2 minutes
Rompingwins 5 minutes
BT 10 minutes.

The question is, what is the shortest amount of time needed for all of them to cross to the other side?

 

[TassieEagle]

Bruce and Richo Cross - 2 minutes
Bruce returns - 1 minute
Rompingwins and BT cross - 10 mins
Richo returns - 2 mins
Bruce and Richo cross again - 2 mins

17 minutes total unless I am missing an easier solution

 

[kickazz]

Bruce and Richo Cross - 2 minutes
Bruce returns - 1 minute
Rompingwins and BT cross - 10 mins
Richo returns - 2 mins
Bruce and Richo cross again - 2 mins

17 minutes total unless I am missing an easier solution

Yep good stuff. Many people get stuck on 18 minutes by focussing on maximising the use of Bruce rather than mi imising the use of the two slow guys.

 

[benchwarmer5]

Try complete this image without taking pen off paper

 

[kickazz]

Try complete this image without taking pen off paper

assuming you can't go over a line twice either....

Do you just pick a corner of the square, trace the outer star shape back to that point, then trace the inner square back to that point again?

 

[benchwarmer5]

assuming you can't go over a line twice either....

Do you just pick a corner of the square, trace the outer star shape back to that point, then trace the inner square back to that point again?

I never solved it to be honest

 

[Kynge of Begrem]

assuming you can't go over a line twice either....

Do you just pick a corner of the square, trace the outer star shape back to that point, then trace the inner square back to that point again?

works for me.

 

[RobbieGray17]

assuming you can't go over a line twice either....

Do you just pick a corner of the square, trace the outer star shape back to that point, then trace the inner square back to that point again?

I did the reverse of that

 

[RobbieGray17]

Bruce and Richo Cross - 2 minutes
Bruce returns - 1 minute
Rompingwins and BT cross - 10 mins
Richo returns - 2 mins
Bruce and Richo cross again - 2 mins

17 minutes total unless I am missing an easier solution

Iév done a similar one with a torch and a bridge, but with I think another variable.

 

[Austin_McCrabbs]

http://www.afl.com.au/news/2015-04-09/motlop-stood-down

 

[humdogg]

Don't read the post below unless you want to know the answer...

Heres one I stumbled across a couple of months ago that I thought was pretty good.

There are four men buried in the sand in a straight line up to their head. There is a wall separating one of them from the other three and every man is wearing a hat. Two men are wearing a white hat and two are wearing a black hat. Each man doesn't know what colour hat they are wearing and they can't turn their head to see what hat every other man is wearing. They can only see the hat of the guys in front of them.

Another man is standing over them with a gun and says that one of them must tell them what colour hat he is wearing or he will shoot them all. If someone makes a wrong guess then the gunman will kill also kill him. One of the buried man shouts out the colour of his hat with total confidence and is correct. So they all get to live.

Which man knew what colour his hat was?

Clues
- The man don't know what order they are in, only that there are two black hats and two white hats.
- No one can see over the wall.
- The man at the back can see both people in front of him but not the man on the other side of the wall.

I'll make a diagram so you can see how the men were all positioned in the sand.

| = wall

B = man with black hat

W = man with white hat

> = direction he is facing


B> | <W <B <W

like this, this is just solid logic rather than some stupid twist.

 

[danger_to_walker]

So, one that's done the rounds recently:

Albert and Bernard just become friends with Cheryl, and they want to know when her Birthday is. Cheryl gives them a list of 10 possible dates.

May 15 May 16 May 19
June 17 June 18
July 14 July 16
August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month, and the day of her Birthday respectively.

Albert: I don't know when Cheryl's Birthday is, but I know that Bernard does not know either.
Bernard: At first I didn't know when Cheryl's Birthday is, but I know now.
Albert: Then I also know when Cheryl's Birthday is.

So, when is Cheryl's Birthday?

 

[kickazz]

So, one that's done the rounds recently:

Albert and Bernard just become friends with Cheryl, and they want to know when her Birthday is. Cheryl gives them a list of 10 possible dates.

May 15 May 16 May 19
June 17 June 18
July 14 July 16
August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month, and the day of her Birthday respectively.

Albert: I don't know when Cheryl's Birthday is, but I know that Bernard does not know either.
Bernard: At first I didn't know when Cheryl's Birthday is, but I know now.
Albert: Then I also know when Cheryl's Birthday is.

So, when is Cheryl's Birthday?

Good one.

Spoiler: my guess

August 17