Hi guys!

Here is a math quiz.
I was carrying a stone weighing 40 kgs. As I was walking thru the road( chilpo bato,rat mato) , my feet slipped and I fell down. The stone broke into 4 pieces. To my suprise, it broke into such pieces that now with the combination of those four pieces of stone , I can weigh any integer number of kgs from 1 to 40. To elaborate, i can weigh 1, 2, 3 ... 40 kgs of rice with the combination of those stones.
U guys need to find out the weights of those four stones...Mathematical proof of the answer will be truely welcomed.

Hey Hauguji ..good try...

I rather solve it in a easier way. Using tristate logic...
In binary there is 1 or 0. but in this trinary or tristate logic there are 3 stages ...-1( if the stone is in another pan) , 0 ( if the stone is not being used) and 1( if the stone is in the right pan while weighing)

since there are 4 stones and 3 logic levels.. there are 3 to the power 4 states(3^4 = 81)..( similar to that of binary where 2^4 states if 4 bits are used)
That gives us 81 states ... of which 40 are negative numbers(since there is -1 logic level), a zero and 40 positive numbers.
These positive 40 numbers are the 40 states or 40 combinations.

so now the weights of each stone ( similar to that of binary) wud be 3^0, 3^1, 3^2 and 3^3.
Thus the weights are 1, 3, 9 and 27.

Kiwi,
I do not have much knowledge about trinary, logics etc? although I can see what you are doing.

Question:
You need to find the value of x and y such that the equation below holds true.
x^2 - 11y! = 2003

(that?s y factorial)

Yea, it is
x = 45 and y=2
Thanks,

how I did is x^2 -11y! =2003 ..............eq (1)
or, x^2 =2003 +11y! and i took y =0 to go to nearest value so
x^2 =2003+11=2014 it gives x = 44.87
Again i took now X=45 and put the value in eq( 1) than I got y= 2

Have fun :)

is x an integer number? if not there are numerous solutions for this equation

it should be integer.

Next:
Question:
How do you write in number 11 hajaar 11 Saya 11. By using only 1s.

Oh yea.
Sorry for missing some info. x and y should be positive integer.

ricky, why thanks?? :)

Regarding the Boat question with Aa, Bb, Cc

Aa crosses the river on the boat, A comes back leaving a
Bb crosses the river, B comes back leaving b
Cc crosses the river, C comes back leaving c

Now,
A and B crosses the river, c comes back
and lastly
Cc goes across and lives happily ever after.

This one is easy one.

If there exists a positive real number x such that Cos[tan(inverse) (x)] = x, find the value of x^2 ( x square).

nhuchche,
>Aa crosses the river on the boat, A comes back leaving a
Bb crosses the river

In this stage, Mr. B will kiss Miss a.

Dada Giri,
Bb goes across the river, b stays there but B comes right back and doesn't have any time to kiss Miss a.

The right answer is:

0.Aa Bb Cc Boat----------------
1.Bb Cc---------------------------Aa Boat
2.A Bb Cc Boat-------------------a
3.A B C ---------------------------a b c Boat
4.A B Cc Boat--------------------a b
5. Cc------------------------------Aa Bb Boat
6.Aa Cc Boat--------------------Bb (returns 2 persons this time which is the key of this question)
7. ac-----------------------------A Bb C Boat
8. abc Boat---------------------ABC
9.a-----------------------------A Bb Cc Boat
10. ab Boat-------------------A B Cc
11. -----------------------------Aa Bb Cc Boat

A B C,
iiiiiiiiiiiiiiiiiiiiii kiss gar arkako GFlai machi*ne haru.

sorry folks, I posted my question on wrong thread. It is in fact not a math question rather is IQ question. The answer goes like this...

First switch on the first switch for 1 minute or so. then switch off the first switch and switch on the second one. Go upstairs... the bulb which is on is the one operated by switch 2, touch either of the off bulbs, the one which is warm is the one operated by the first switch and the cold one is the one operated by the third switch..

Guji,
Hints deu na yaar. katti gahro chha baaa....

3 dimensions ma garne hola.
Ki solid angle nikalnu parchha yaar?

Three dimension hoina, baru you have to reduce it to two dimension.
Hints: Cut the cone along PV.
You ultimately have to figure out some angle--willl leave the rest to you.

Good luck!!!

Guji,

La baji diye.
Mero taauko khayo raun nai fulyo 1uta 2uta ta.

four pieces: 1, 5, 10, and 10..
1 = 1
2 = 1+1
3 = 1+1+1 ( you weigh 1 kg, take if out, weigh another, take it out, weigh the third one, and combine the three;))
...
39 = 1+1+1+1+5+(10+10)+10
40 = (10+10) + (10+10)

there you go.... it might now be the answer you were looking for.. but oh well... you can weight whatever you want with that now.... PROVE ME WRONG.... ahah

ahah, i am so dumb... i forgot that we started from 40 kg... so i would like to correct my mistake;)

four pieces originated from the 40 kg stone: 1, 5, 15, 19
and again.. the same pattern, same technique, lol

1 = 1
2 = 1+1
3 = 1+1+1
4 = 1+1+1+1
5 = 5
....
....
39 = 5+15+19
40 = 5+15+19+1

now, you can always have the stone with different weight, but it just depends upon how much time you wanna waste weighing that damn rice..... ahha

sand is deep, your answer is not quite correct. from what i understand, you have exactly 4 stones, each of a different weight. so you cannot keep four 1kg "types" to weight 4kg's. from kiwiland's answer is the best - don't know if there is another answer. with his approach, you can measure all weights up to 40 using just those 4 stones, PROVIDED you are using a mass balance(taraju). for example, to measure 2kg's, you keep the one 3kg stone on one side and the one 1kg on the side of the rice. using various combinations, you should be able to measure up to 40 kg's.

Let me try, the #'s should be 2+3+7+28=40 and it is suposed to work like
3-2 =1
2 = 2
3 = 3
7 - 3 = 4
2+3 = 5
7 + 2 - 3 = 6
7 = 7
7+ 3 -2 = 8
7 + 2 = 9
7 + 3 = 10
thereafter adding seperately the weight generated from above method
10 +1 =11 and so on.
Since the conditions are not set, I believe this one also serves the purpose of weighing up to 40 Kgs.