A morning maths puzzle
A morning maths puzzle
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Discussion

ILikeCake

Original Poster:

420 posts

174 months

Tuesday 9th October 2018
quotequote all
I am changing careers and am ears deep in a maths text book. The book has questions at the end of each chapter, but gives no workings of the answer.

The question is:
Amy, Jim, John and Kelly are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 3, 6, and 9 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
What is the shortest time for moving all four people to the other side of the river?

The shortest time I can get to is 20 minutes. The answer in the book is 19 minutes... discuss!

TwigtheWonderkid

49,124 posts

180 months

Tuesday 9th October 2018
quotequote all
Amy and Jim go over, that takes 3 mins.
Amy rows back alone, 1 min
John and Kerry go over, 9 mins
Jim rows back alone to get Amy, 3 mins
Jim & Amy cross back, 3 mins

Job done in 19 mins.

Blatter

916 posts

221 months

Tuesday 9th October 2018
quotequote all
ILikeCake said:
I am changing careers and am ears deep in a maths text book. The book has questions at the end of each chapter, but gives no workings of the answer.

The question is:
Amy, Jim, John and Kelly are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 3, 6, and 9 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
What is the shortest time for moving all four people to the other side of the river?

The shortest time I can get to is 20 minutes. The answer in the book is 19 minutes... discuss!
Have just seen the previous reply, so scrub my answer................

ILikeCake

Original Poster:

420 posts

174 months

Tuesday 9th October 2018
quotequote all
Oh, maybe I should put the career change on hold wobble

Okay if that was too easy how about this:

You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?

TwigtheWonderkid

49,124 posts

180 months

Tuesday 9th October 2018
quotequote all
The key to these type of questions is always to get the two slowest people over together. John and Kerry going over separately will take 15 mins, but getting them over together will only take 9. Once you've realised you've got to get them over together to make the shortest time, you can work the rest of the puzzle around that.

You need to get the 2 quickies over, then send one back with the canoe, then send the 2 slowies over, then the quicky left on the far bank comes back to collect the other quicky now on the near bank, and both quickies return to join the 2 slowies and complete the task.

TwigtheWonderkid

49,124 posts

180 months

Tuesday 9th October 2018
quotequote all
ILikeCake said:
Oh, maybe I should put the career change on hold wobble

Okay if that was too easy how about this:

You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Ooo, I've heard this one years ago, with 2 eggs and 100 floors. I can't remember the algebra, but to get the best outcome was starting at floor 15, then increasing in stages of 1 less floor each time, so floor 15, then +14 to floor 29, plus 13 to floor 42, plus 12 to floor 54, floor 65, 75, 84 and so on. The once the first egg breaks, go up in stages of 1 from the last successful drop.

Or something like that. I'm too old for all this stuff now. .

SlackBladder

2,654 posts

233 months

Tuesday 9th October 2018
quotequote all
TwigtheWonderkid said:
Amy and Jim go over, that takes 3 mins.
Amy rows back alone, 1 min
John and Kerry go over, 9 mins
Jim rows back alone to get Amy, 3 mins
Jim & Amy cross back, 3 mins

Job done in 19 mins.
Am I being thick here, but when Jim & Amy cross back then that would be 1 minute and therefore a total of 17 mins?

indigochim

2,083 posts

160 months

Tuesday 9th October 2018
quotequote all
SlackBladder said:
Am I being thick here, but when Jim & Amy cross back then that would be 1 minute and therefore a total of 17 mins?
ILikeCake said:
......the slower person dictates the crossing time.

Wacky Racer

41,363 posts

277 months

Tuesday 9th October 2018
quotequote all
How about this one, it's surprising how many intelligent people get it wrong.

In a bedroom drawer there are 20 loose red socks and 20 blue socks.

If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?

daddy cool

4,107 posts

259 months

Tuesday 9th October 2018
quotequote all
ILikeCake said:
Okay if that was too easy how about this:

You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Probably highlighting myself as thick, but is it "one"?
ie, if you drop one ball from the 1st floor, and it dents, then you wouldn't use the 2nd and you wouldn't go any higher than the 1st floor?

daddy cool

4,107 posts

259 months

Tuesday 9th October 2018
quotequote all
Wacky Racer said:
How about this one, it's surprising how many intelligent people get it wrong.

In a bedroom drawer there are 20 loose red socks and 20 blue socks.

If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
3?

JuniorD

9,013 posts

253 months

Tuesday 9th October 2018
quotequote all
Wacky Racer said:
How about this one, it's surprising how many intelligent people get it wrong.

In a bedroom drawer there are 20 loose red socks and 20 blue socks.

If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
Three?

Wacky Racer

41,363 posts

277 months

Tuesday 9th October 2018
quotequote all
daddy cool said:
3?
Yes, the amount of people that say 21 is amazing...….try it on your friends.

m1dg3

128 posts

184 months

Tuesday 9th October 2018
quotequote all
Wacky Racer said:
How about this one, it's surprising how many intelligent people get it wrong.

In a bedroom drawer there are 20 loose red socks and 20 blue socks.

If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
21

m1dg3

128 posts

184 months

Tuesday 9th October 2018
quotequote all
Wacky Racer said:
Yes, the amount of people that say 21 is amazing...….try it on your friends.
Oh yeah, doh! 21 to guarantee an unmatched pair!

MYOB

5,126 posts

168 months

Tuesday 9th October 2018
quotequote all
Wacky Racer said:
Yes, the amount of people that say 21 is amazing...….try it on your friends.
I would have said 2. I could pick up a matching pair in the first two picks. But I'm not a maths genius!

PositronicRay

29,013 posts

213 months

Tuesday 9th October 2018
quotequote all
Is your new career as a canoeist?

daddy cool

4,107 posts

259 months

Tuesday 9th October 2018
quotequote all
MYOB said:
Wacky Racer said:
Yes, the amount of people that say 21 is amazing...….try it on your friends.
I would have said 2. I could pick up a matching pair in the first two picks. But I'm not a maths genius!
Its not "number of picks", its number of individual socks you take out the drawer.
Pick a sock - its (say) Red.
Pick a 2nd sock - if its red, great, you win, game over. If its blue, you have an unmatched pair - move to round 3.
Pick a 3rd sock - whether its red or blue you now have 1 matching pair when combined with the Red from round 1, and the Bue from round 2.

TwigtheWonderkid

49,124 posts

180 months

Tuesday 9th October 2018
quotequote all
MYOB said:
Wacky Racer said:
Yes, the amount of people that say 21 is amazing...….try it on your friends.
I would have said 2. I could pick up a matching pair in the first two picks. But I'm not a maths genius!
"Ensure" is the key word in the question. 3 is the minimum amount to ensure a matching pair. 2 is the minimum number to possibly get a matching pair.

daddy cool

4,107 posts

259 months

Tuesday 9th October 2018
quotequote all
ILikeCake said:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Come on then, don't leave me in suspenders...