# Spring Weeks 2012 Thread watch

1. (Original post by miml)
The clock problem is solved easily in the general case with some simple maths.

Another one I've heard about is when do two hands of a clock overlap (again it's just a specific case of the above)

Brainteasers in general are the best part of an interview for me as you generally know if you've answered the question right. Whereas with competency questions (especially in telephone interviews) it's difficult to judge how well you may be doing.
had this in one of my oxford interviews ahah
2. (Original post by Marc Fiorano)
The only thing that got me thinking about the way you've phrased the question is that it says the time on YOUR watch is 5:15, not the time on the wall clock itself. So you either go off in the assumption that the time on your watch is identical to that on the wall clock or you answer the question with a question, asking whether the wall clock is indeed also showing 5:15am.
Well yes, I implied that you are at this second watching your watch and at the same time look at the wall clock. Wasn't formulated that good, I know. Be indulgent with me, I'm not an english speaking person :P
3. Another one I've heard about is when do two hands of a clock overlap (again it's just a specific case of the above)
How is that meant? How would you answer? just at 12.00?
4. (Original post by jevira)
How is that meant? How would you answer?
By the way, since no one answered the question properly. 67.5.
5. (Original post by jevira)
How is that meant? How would you answer?
For example at 12:00 the two hands overlap (angle between them is 0). When does this happen again? How many times does it happen in 24 hours?
6. (Original post by jevira)
Well, here's one more for you:

Let's say our watch is telling us that it is 5.15 pm. Now on a wall clock, what would be the angle between the two clock hands?
15mins is at 90deg.
5 is at 360*5/12 = 150deg
6 is at 180deg
1/4 dist = 157.5deg

157.5-90 = 67.5deg

Lol at me for not refreshing the page for 20 mins then typing this really quickly.
7. (Original post by miml)
For example at 12:00 the two hands overlap (angle between them is 0). When does this happen again? How many times does it happen in 24 hours?
I'd make this more intuitive: the two hands overlap in every hour once. Just not on the step from 11.00 to 12.00 because the hour-hand reaches 12.00 again a bit earlier than the minute-hand. So 12-1 = 11 times on a half day. 22 in a full day.

A king has a wine cellar with 250 bottles of expensive wine in it.

He receives a note that someone has put a drop of poison in one of his bottles of wine at random making one drop of the wine enough to kill someone 30 days after they drink the wine.

He happens to find eight prisoners who have been sentenced to death in 2 months and knows that he could just use these prisoners beforehand to help him work out which wine bottle is poisoned.

How does he do it?
9. (Original post by jevira)
I'd make this more intuitive: the two hands overlap in every hour once. Just not on the step from 11.00 to 12.00 because the hour-hand reaches 12.00 again a bit earlier than the minute-hand. So 12-1 = 11 times on a half day. 22 in a full day.
Agreed. But doesn't answer the first part - when?

I won't answer the wine question, but a little hint
Spoiler:
Show
2^8 = 256

I imagine Comp Sci students should be good at this one.
10. (Original post by I'mSet)

A king has a wine cellar with 250 bottles of expensive wine in it.

He receives a note that someone has put a drop of poison in one of his bottles of wine at random making one drop of the wine enough to kill someone 30 days after they drink the wine.

He happens to find eight prisoners who have been sentenced to death in 2 months and knows that he could just use these prisoners beforehand to help him work out which wine bottle is poisoned.

How does he do it?
It would be so much easier if you would only need to limit down the bottle number to say 5. I mean, come on, he's a king, surely he'd rather throw away 5 bottles than make somone think up of a way to find the very same one with a chance of mixing things up and effectively killing him!
11. (Original post by I'mSet)

A king has a wine cellar with 250 bottles of expensive wine in it.

He receives a note that someone has put a drop of poison in one of his bottles of wine at random making one drop of the wine enough to kill someone 30 days after they drink the wine.

He happens to find eight prisoners who have been sentenced to death in 2 months and knows that he could just use these prisoners beforehand to help him work out which wine bottle is poisoned.

How does he do it?
I assume it's exactly 30 days, not more, not less until they die.

Since there are 250 bottles and 8 prisoners, every prisoner drinks a glass of one wine on one day, this making 29 times. (So that they die before they will be executed, if they would have drunk the wine with poison). One should clearly write down which prisoner when drank which whine so that the poissoned bottle can be detected.
After this, this would make 232 bottles tested, remaining 18 untested. As a king who surely is rich, I would wait for some other prisoners who've been sentenced to death or just not open/drink these 18 bottles (if no prisoner has died of drinking the wine. in that case, the remaining 18 bottles all are safe.)
12. (Original post by jevira)
I assume it's exactly 30 days, not more, not less until they die.

Since there are 250 bottles and 8 prisoners, every prisoner drinks a glass of one wine on one day, this making 29 times. (So that they die before they will be executed, if they would have drunk the wine with poison). One should clearly write down which prisoner when drank which whine so that the poissoned bottle can be detected.
After this, this would make 232 bottles tested, remaining 18 untested. As a king who surely is rich, I would wait for some other prisoners who've been sentenced to death or just not open/drink these 18 bottles (if no prisoner has died of drinking the wine. in that case, the remaining 18 bottles all are safe.)
Close, there is a better way though.
13. (Original post by I'mSet)
15mins is at 90deg.
5 is at 360*5/12 = 150deg
6 is at 180deg
1/4 dist = 157.5deg

157.5-90 = 67.5deg

Lol at me for not refreshing the page for 20 mins then typing this really quickly.
The angle between the hands at 5:15 is 60 deg.

Between each hour point the angle is 30deg (360/12).

5:15 is one hand at 3, one hand at 5..two points between = 30 x 2 = 60 deg.

EDIT: Just realised this is wrong fml....my mechanics professor would be piissssssed
14. (Original post by I'mSet)
Close, there is a better way though.
C'mon, it's a sympathetic reasoning, isn't it? Haha
15. (Original post by jevira)
C'mon, it's a sympathetic reasoning, isn't it? Haha
Solution below:

Spoiler:
Show
You name prisoners from 1 to 8 and stand them in a line.

As previously said 2^8 is 256, meaning that in binary, you can count up to 256 with 9 digits. Anything less (such as 250), requires only 8 digits.

You assign each bottle a number from 1 - 250.

For each bottle, you convert it's reference into a binary number (for example the 8th bottle would be 00001000.

You translate 1 = taking a sip and 0 = not taking a sip. (for example the 8th bottle would be drunk by prisoner 4 only).

Go through all the bottles.

On day 31, wait for a selection of your 8 prisoners to die.

Work out who died.

Convert the digits of the people who died from binary into the base 10 number.

Feed the other prisons your chosen bottle.

Assuming you choose two months with 31 days, check they die on day 62.

If you don't have two months with 31 days, then watch them die anyway.
16. Stupid question with a much more stupid answer, haha I would have never come up with such an idea.

"Check they die on day 62" -> you cant check day 62 since they are being executed on day 60 (assuming 1 month = 30 days), so you can't observe these 2 days more.
17. (Original post by I'mSet)
Solution below:

Spoiler:
Show
You name prisoners from 1 to 8 and stand them in a line.

As previously said 2^8 is 256, meaning that in binary, you can count up to 256 with 9 digits. Anything less (such as 250), requires only 8 digits.

You assign each bottle a number from 1 - 250.

For each bottle, you convert it's reference into a binary number (for example the 8th bottle would be 00001000.

You translate 1 = taking a sip and 0 = not taking a sip. (for example the 8th bottle would be drunk by prisoner 4 only).

Go through all the bottles.

On day 31, wait for a selection of your 8 prisoners to die.

Work out who died.

Convert the digits of the people who died from binary into the base 10 number.

Feed the other prisons your chosen bottle.

Assuming you choose two months with 31 days, check they die on day 62.

If you don't have two months with 31 days, then watch them die anyway.
Interesting, but I think it would be rare to think of this on the spot.

EDIT: to above. You don't need to wait for the 62 day, it's just a way of killing.
18. (Original post by I'mSet)
Solution below:

Spoiler:
Show
You name prisoners from 1 to 8 and stand them in a line.

As previously said 2^8 is 256, meaning that in binary, you can count up to 256 with 9 digits. Anything less (such as 250), requires only 8 digits.

You assign each bottle a number from 1 - 250.

For each bottle, you convert it's reference into a binary number (for example the 8th bottle would be 00001000.

You translate 1 = taking a sip and 0 = not taking a sip. (for example the 8th bottle would be drunk by prisoner 4 only).

Go through all the bottles.

On day 31, wait for a selection of your 8 prisoners to die.

Work out who died.

Convert the digits of the people who died from binary into the base 10 number.

Feed the other prisons your chosen bottle.

Assuming you choose two months with 31 days, check they die on day 62.

If you don't have two months with 31 days, then watch them die anyway.
im pretty sure a question like that would not come up in an interview
19. (Original post by Banker91)
im pretty sure a question like that would not come up in an interview
I got it in my interview. Wasn't for a Spring week though.
20. (Original post by I'mSet)
I got it in my interview. Wasn't for a Spring week though.
At which company?

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