Riddles Options

[Nimii]

MTM u singing KS song so now u wont get any sunset, na koi dil na koi player ! Samjhus

[shivani]

here's one ....

Let ABC be an equilateral triangle. Let E be the set of the points of
the sides AB, BC and CA. Partition the set E to two sets E_1 and E_2.
Prove or disprove:
There is always a right triangle having all its vertices in one of
the two sets.

[divz]

here's one ....

Let ABC be an equilateral triangle. Let E be the set of the points of
the sides AB, BC and CA. Partition the set E to two sets E_1 and E_2.
Prove or disprove:
There is always a right triangle having all its vertices in one of
the two sets.

coming here after long time..... just one querry .. E is set of o many points... ???? we cam assume or there is some constraint... ?

pardon me if i am at any folly..!!

[shivani]

Reviving the thread on Anil's demand : ).

A simple one, just to get back in shape..

Make 68 using 1, 2, 8, and 9. Each number must be used only once and permissable actions are +,-,*, /.

[Mandrake]

(9-2-1)and 8 = 6 and 8 = 68

[shivani]

(9-2-1)and 8 = 6 and 8 = 68

"=" operator is not listed in the list, and cannot be used. Only valid operators are + , - , * , /. Use of paranthesis is allowed though

[vivekpm]

72-4=68
this gives 9*8-4 = 9*8-8/2
= 8 * (9 - 1/2)

Cheers,

[shivani]

correcto Vivek

And you were supposed to give the next one.. but.. this time on your behalf
A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

[Anil4]

Shivani, firstly thanks for reviving this thread at my request. I thought that with an influx of new members, it was time to revive some great threads of the past, to provide an opportunity to these new members to participate.

I have wrestled with your riddle but dont have a solution yet.

1st Student -- all 1000 lockers are open.

2 nd Student - 500 lockers are closed.

This is where it gets interesting and I'm hoping the resident mathematician of HF, Vivek, will spot some trend. The third student will close the third locker which was opened by the first student, will open the sixth locker which was closed by the second student and so on.

I think the answer to the riddle is in identifying which lockers get handled an odd ( as opposed to even) number of times, so that after opening, closing, opening etc, they remain open when the thousandth student has done his bit.

Vivek, I have done the hard part, now put it as a mathematical equation, and solve it.

Anil

[shivani]

I think the answer to the riddle is in identifying which lockers get handled an odd ( as opposed to even) number of times

You are moving in the right direction : ).

And thanks for reminding and participating in the thread Anil, for without enthusiastic participants, there cant be no fun

[Mandrake]

Anil, you are ignoring the most consistent replier here. Without my lateral thinking solutions, Vivek would run away with the 1st prize (that he does anyways, is besides the point).

So here are my 1000 bits.
The 1000th student JUST DOESN"T CARE!!
He is fed up with the childish stupidity of the principal (imagine, the principal, of all the people! Gawd!!) playing silly games like these. Arey! Doosra koi dhandha nahi hai kya? Ek ko bolo 'kholo', ek ko 'band'....
He watches incredulously for a bit, whips out his cell-phone and calls up dad.
Within a short time the Mental Hospital Van comes and escorts the principal away.
The student is admitted to another school without any further delay. (On the way, there is a precautionary stop-over at the psychologist to check whether the incident has left any scars on the student's mind).

Back in the school, the janitor goes and shuts all the lockers one by one, muttering under the breath about how the education system is going to the dogs...

(By the way, at 10 seconds per locker (+ proceeding to the next locker) he spends almost three hours shutting the 1000 lockers...)

[august]

I think the answer to the riddle is in identifying which lockers get handled an odd ( as opposed to even) number of times

You are moving in the right direction : ).

And thanks for reminding and participating in the thread Anil, for without enthusiastic participants, there cant be no fun

so after 20 students, lockers tht are still open- 1, 4 ,9 and 16.

oddly enough, these were the lockers handled by odd number of students.

[snita]

some pattern involving perfect squares....?

[vivekpm]

You are right snita. Shivani, wasn't there a similar problem posted before?

Cheers,

[vivekpm]

For, why it is perfect squares, check this out http://www.hamaraforums.com/index.php?show...5575&st=15#

Cheers,