Riddles Options

[shivani]

1. Guess the next number

77 58 49 45 29 27 23

[shivani]

ok! a clue.. only need to look at the current number to find the next number

[vivekpm]

Ok... I think I have got it. But I cannot help but curse you since you made me spend good 30 minutes of my morning time on numbers and I still have to read other posts on HF

Just Kidding... numbers are my weakness...

77: 7*7 = 49 + 9 = 58
58: 5*8 = 40 + 9 = 49
49: 9*4 = 36 + 9 = 45
45: 4*5 = 20 + 9 = 29
29: 2*9 = 18 + 9 = 27
27: 2*7 = 14 + 9 = 23
23: 2*3 = 6 + 9 = 15

So 15 is the answer...

Cheers,

[shivani]

sweet Vivek : ) .. I took a whole day to crack it
Now next one.. its simpler..

2. There are 9 accountants on a round table. They need to find out their average salary without divulging their own slaary to anyone else. There is only pen and paper available and nothing else..

[vivekpm]

sweet Vivek : ) .. I took a whole day to crack it
Now next one.. its simpler..

2. There are 9 accountants on a round table. They need to find out their average salary without divulging their own slaary to anyone else. There is only pen and paper available and nothing else..

Will have to admit that your clue helped. Had I looked at the problem before you posted the clue and if you had not said that look at the current number then I would have tried to find the relation between 1st and 2nd or 1st and 3rd number and so on. But since you said current number, I started taking sums and products of each number. All such problems are "Aha" problems. You can crack them in minutes if you are lucky or you can take hours before you arrive at a solution. Numbers amaze me a lot. There is always a pattern to look out for in them.

Will give a try on the accountant problem. Its tempting to try now but will restrain myself till evening. Though there will be a thread running all the time.

Cheers,

[vivekpm]

Thought over this during lunch and here is how I would do this,

I will be the first person and write down a number on paper which obviously will not be my salary. Then I will pass on this paper to each of the remaining 8 accountants and ask them to add their salary to it and erase previous figure and note down the new figure.

At the end, I will subtract the number I had noted down initially and add my salary and divide the sum by 9.

Looks like a crude way but I cannot think of a formal solution as of now. I hope "round table" is just to confuse and the problem does not have an element of Geometry in it...

Cheers,

[visuja]

Brilliant Vivek Excellent solutions to both puzzles .... Very well done

[shivani]

Vivekahh.. Korrect again.. and you get another one in the prize
..or whoever cares to solve actually
3. You have two ropes and each take 1 hour to burn completely. They burn at non unifrom rate.
How would you measure 15 minutes using these two ropes?

[vivekpm]

Vivekahh.. Korrect again.. and you get another one in the prize
..or whoever cares to solve actually
3. You have two ropes and each take 1 hour to burn completely. They burn at non unifrom rate.
How would you measure 15 minutes using these two ropes?

Thanks Shivani (and thanks Vivek for the compliment). But I guess I got lucky with first problem. Second one was a little easier. And now this third one, I won't answer because I had solved this problem long ago. This was asked to me in an interview.

Cheers,

[shivani]

chalo vivek aapke liye ek aur sahi : )
4. There are 100 closed doors. 1st person who comes, opens all doors. 2nd person changes the current state of every 2nd door (opens closed door and closes open door). 3rd person changes state of every 3rd door, starting from 3rd door. This continues till 100th person. Finally how many doors are open and how many closed..

[visuja]

maybe im making an assumption here, but its not very clear to me -- what that assumption is. Nevertheless, heres a solution:

Since a rope takes an hour to burn, if that rope is lit from both ends, the entire rope will take only half an hour to burn completely, irrespective of the rate at which each segment burns. So now, by the same logic, if the rope is lit at each quarter of its length, the entire rope should be burnt in 15 minutes.

Then why is the second rope required !??

[shivani]

Korrect Visu baba

[vivekpm]

chalo vivek aapke liye ek aur sahi : )
4. There are 100 closed doors. 1st person who comes, opens all doors. 2nd person changes the current state of every 2nd door (opens closed door and closes open door). 3rd person changes state of every 3rd door, starting from 3rd door. This continues till 100th person. Finally how many doors are open and how many closed..

Seems you are determined to get me fired from my job

Writing a small program gave me "10" as answer (open doors). I will get back with the logic soon. Obviously door which has been touched odd number of times remains open. Will have to find out what are the special properties of 10 such numbers between 1 and 100. Will be back.

Cheers,

[vivekpm]

chalo vivek aapke liye ek aur sahi : )
4. There are 100 closed doors. 1st person who comes, opens all doors. 2nd person changes the current state of every 2nd door (opens closed door and closes open door). 3rd person changes state of every 3rd door, starting from 3rd door. This continues till 100th person. Finally how many doors are open and how many closed..

Seems you are determined to get me fired from my job

Writing a small program gave me "10" as answer (open doors). I will get back with the logic soon. Obviously door which has been touched odd number of times remains open. Will have to find out what are the special properties of 10 such numbers between 1 and 100. Will be back.

Cheers,

Just learnt that only perfect squares can have odd number of divisors. This is because all other numbers can only have pair of divisors. Take for example, 12, it has three pairs of divisors, "2, 6", "1, 12" and "4,3". Only perfect squares can have odd number of divisors because its square-root cannot pair up with any other number. Take for example 49, its divisors are "1, 49" and "7". And since there are 10 perfect squares between 1 and 100, there will be 10 doors open.

Interesting concept. Learnt a new thing about perfect squares today

Cheers,

[shivani]

ayoooo Vivekah..
am getting slightly scared of u now..
u r an evil mathematician !!
ye lo ..since you love maths so much
5. A car has a journey of 78 miles to make.
The first half of the journey is uphill, and the second half downhill.
He averages 30 miles an hour to the top of the hill.
How fast must he go down the hill to average 60 miles per hour?