PG Premier League - Chennai Dream Team

[nishant_rungta]

Originally Posted by maverick_srikan

What if the driver gets back home at 6PM. He travels for half an hour, picks the boss up at 5.30PM and reaches home at 6PM. The boss leaves at 4.30PM. Does this violate any of the conditions given in the question?

I had mentioned in the question... ASSUME THAT THE SPEEDS ARE CONSTANT..


Nishant

[satanica]

Originally Posted by satanica

...When Mr and Mrs Thompson gave a dinner-party, they invited Mr and Mrs Johnson, Mr and Mrs Edmundson, Mr and Mrs Richardson and Mr and Mrs Stevenson. The ten people were seated at a circular table, and no man sat next to his own wife. Mr Thompson sat next but one to Mrs Stevenson. Mr Edmundson sat between two ladies, and so did Mr Richardson. Mrs Johnson sat next to her sister, while Mr Johnson sat next but one to Mr Stevenson, who was immediately to the left of his father-in-law. Mrs Edmundson sat next but two to her husband, and Mrs Johnson sat next but two to Mrs Richardson. Three of the ladies each sat between two men. Can you say in what order the ten people were seated at the table?

Originally Posted by sid_dharth

I tried solving this puzzle and attached is the solution

Cheers!!!
Siddharth

I think you misunderstood the part which says 'Three of the ladies each sat between two men.'. This means that there were three ladies each of whom sat between two men. It does not mean that a group of three ladies was sitting between two men. Your solution fails for this criterion.

BTW, I have solved this and hence, now I have the solution for this problem. If anyone wants the same, let me know.

[maverick_srikan]

Originally Posted by nishant_rungta

I had mentioned in the question... ASSUME THAT THE SPEEDS ARE CONSTANT..


Nishant

I still don't get the idea.

Take this for example. Let the entire distance be 30 and the car travel at 30 kmph.

The car travels for 30 mins either way, covering 15 kms up and down.

The boss starts at 4.30 and walks at 15 kmph for 1 hour, and is picked up after 1 hour by the car.

The boss starts at 4.30, walks at 15 kmph and gets picked up at 5.30.

Am I missing something or does the question assume that Vikas starts from the office at 5 PM?

[satanica]

Originally Posted by maverick_srikan

What if the driver gets back home at 6PM. He travels for half an hour, picks the boss up at 5.30PM and reaches home at 6PM. The boss leaves at 4.30PM. Does this violate any of the conditions given in the question?

That would not make any difference.

The question states that 'Today, however, Vikas left early and started walking towards his house, at the same time the driver started from his house towards the office.'. If Vikas starts at 4:30 then the driver also starts at 4:30. The questions also states that 'However, in all this, Vikas's travel time increased by half an hour.' which means that their travel time now is 1.5 hours rather than 1 hour.
The time of starting here is inconsequential. The only points to note are:
1. the speeds are constant
2. both Vikas and the driver start at same time
3. the time of travel is 1.5 hours
These are enough to give you the answer as 45 minutes.

[nishant_rungta]

Originally Posted by maverick_srikan

I still don't get the idea.

Take this for example. Let the entire distance be 30 and the car travel at 30 kmph.

The car travels for 30 mins either way, covering 15 kms up and down.

The boss starts at 4.30 and walks at 15 kmph for 1 hour, and is picked up after 1 hour by the car.

The boss starts at 4.30, walks at 15 kmph and gets picked up at 5.30.

Am I missing something or does the question assume that Vikas starts from the office at 5 PM?

Ahhh let me explain... The question says assume constant speeds.. Well forget this point.

Initially the car completes the affair in 1 hour.
Next time, the car completes the whole affair in 1.5 hrs is what the problem says. Clearly, it means that the car is late and is not travelling at the same speed which it had earlier. I mean when it completes the journey in 1.5 hrs, it is late by 30 mins. Hence, when I say that the speeds are constant what i mean is the speed with wihch it travels in any journey is constant.

In this case, it travelled for 45 mins on each segment. When it reached Vikas in 45 mins and when both started at the same time from their respective places, its obvious that Vikas walked for 45 mins. Hope u get the point now..

As i mentioned earlier. Guys like us preparing for cat have started to complicate things drastically. Think simple, think straight


Nishant

[maverick_srikan]

Originally Posted by satanica

That would not make any difference.

The question states that 'Today, however, Vikas left early and started walking towards his house, at the same time the driver started from his house towards the office.'. If Vikas starts at 4:30 then the driver also starts at 4:30. The questions also states that 'However, in all this, Vikas's travel time increased by half an hour.' which means that their travel time now is 1.5 hours rather than 1 hour.
The time of starting here is inconsequential. The only points to note are:
1. the speeds are constant
2. both Vikas and the driver start at same time
3. the time of travel is 1.5 hours
These are enough to give you the answer as 45 minutes.

Precisely! The point that i missed was that they start at the same time!

If they start at the same time, the time when they meet will be equal => time taken for total journey/2=>90/2=45 minutes

Talk about being plain silly!

[maverick_srikan]

Originally Posted by nishant_rungta

Ahhh let me explain... The question says assume constant speeds.. Well forget this point.

Initially the car completes the affair in 1 hour.
Next time, the car completes the whole affair in 1.5 hrs is what the problem says. Clearly, it means that the car is late and is not travelling at the same speed which it had earlier. I mean when it completes the journey in 1.5 hrs, it is late by 30 mins. Hence, when I say that the speeds are constant what i mean is the speed with wihch it travels in any journey is constant.

In this case, it travelled for 45 mins on each segment. When it reached Vikas in 45 mins and when both started at the same time from their respective places, its obvious that Vikas walked for 45 mins. Hope u get the point now..

As i mentioned earlier. Guys like us preparing for cat have started to complicate things drastically. Think simple, think straight


Nishant

Not so much about complicating things, but more about missing conditions

[nishant_rungta]

Originally Posted by satanica

I think you misunderstood the part which says 'Three of the ladies each sat between two men.'. This means that there were three ladies each of whom sat between two men. It does not mean that a group of three ladies was sitting between two men. Your solution fails for this criterion.

BTW, I have solved this and hence, now I have the solution for this problem. If anyone wants the same, let me know.

Satan... We guys are awaiting the solution to this problem big time

I had a tough time doing that

PS: Solve this. Simple one again

A number is said to be a "self-content number" if sum of the factorials of its digits is the number itself. Find the middle digit of a three-digit self-content number with all distinct digits.

[satanica]

Originally Posted by nishant_rungta

Satan... We guys are awaiting the solution to this problem big time

I had a tough time doing that ...

Question
When Mr and Mrs Thompson gave a dinner-party, they invited Mr and Mrs Johnson, Mr and Mrs Edmundson, Mr and Mrs Richardson and Mr and Mrs Stevenson. The ten people were seated at a circular table, and no man sat next to his own wife. Mr Thompson sat next but one to Mrs Stevenson. Mr Edmundson sat between two ladies, and so did Mr Richardson. Mrs Johnson sat next to her sister, while Mr Johnson sat next but one to Mr Stevenson, who was immediately to the left of his father-in-law. Mrs Edmundson sat next but two to her husband, and Mrs Johnson sat next but two to Mrs Richardson. Three of the ladies each sat between two men. Can you say in what order the ten people were seated at the table?

Solution
(in clockwise order round the table)
Mrs Stevenson
Mrs Johnson
Mr Thompson
Mr Stevenson
Mrs Richardson
Mr Johnson
Mrs Edmundson
Mr Richardson
Mrs Thompson
Mr Edmundson

PS: Start from the fact that two men and two women are seated together. And then apply the fact that 'Mr Stevenson, who was immediately to the left of his father-in-law'.

Originally Posted by nishant_rungta

...PS: Solve this. Simple one again

A number is said to be a "self-content number" if sum of the factorials of its digits is the number itself. Find the middle digit of a three-digit self-content number with all distinct digits.

Obviously one of the digits is 5. 6 is not possible as 6!=720 and we'll have atleast a 7 in number which will contradict the fact that the number is less than 1000.
5!=120 and 4!=24 means that the number is less than 200 and hence the first digit is 1.
100+10b+c=120+1+x!
10b+c=21+x! (x<5)
c=5
10b=16+x!
which means that x! ends in 4. The only possible value of x is 4 which gives b=4.

The number is 145.

PS: Such numbers are called 'Factorions' and there are only 4 such numbers.

[nishant_rungta]

Originally Posted by satanica

PS: Such numbers are called 'Factorions' and there are only 4 such numbers.

Exactly and they are:

A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers: