Two players play a game using the interval [0,33] on the x-axis. The first player randomly chooses a square of side length s∈Z+, which has a side that lies entirely on the interval. The second player randomly chooses a circle with radius r∈Z+, which has a diameter that lies entirely on the interval. After repeating choosing random squares and circles in this fashion, the players realize that the probability that the circle and square intersect is 12. Let S={(s,r):probability of intersection is 12}. Determine ∑(s,r)∈S(s+r). Clarification of notation: The set S is the set of all ordered pairs of integers, (s,r), such that the probability that a square of side length s and a circle of radius r will intersect is 12.
Two players play a game using the interval [0,33] on the x-axis. The first player randomly chooses a square of side length s∈Z+, which has a side that lies entirely on the interval. The second player randomly chooses a circle with radius r∈Z+, which has a diameter that lies entirely on the interval. After repeating choosing random squares and circles in this fashion, the players realize that the probability that the circle and square intersect is 12. Let S={(s,r):probability of intersection is 12}. Determine ∑(s,r)∈S(s+r). Details and assumptions Clarification of notation: The set S is the set of all ordered pairs of integers, (s,r), such that the probability that a square of side length s and a circle of radius r will intersect is 12.
Two players play a game using the interval [0,33] on the x-axis. The first player randomly chooses a square of side length s∈Z+, which has a side that lies entirely on the interval. The second player randomly chooses a circle with radius r∈Z+, which has a diameter that lies entirely on the interval. After repeating choosing random squares and circles in this fashion, the players realize that the probability that the circle and square intersect is 12. Let S={(s,r)robability of intersection is 12}. Determine ∑(s,r)∈S(s+r). Details and assumptions Clarification of notation: The set S is the set of all ordered pairs of integers, (s,r), such that the probability that a square of side length s and a circle of radius r will intersect is 12.
expand the term as (3^512+1)*(3^256+1)*(3^128+1)*(3^64+1)*(3^32+1)*(3^16+1)*(3^8+1)(3^4+1)(3^2+1)(3+1)(3-1) these terms are divisible by 2 and (3^256+1) is divisible by 4Answer 12
answer cant be 12 bro!!!!
coz if n=12, then 2n=24 which means that the number 3^1024-1 should be divisible by 24, which in turn means that it shold be divisible by 3
But we can see that 3^1024-1 can never be divisible by 3 as it will always leave a remainder of 2 when divided by 3
answer cant be 12 bro!!!!coz if n=12, then 2n=24 which means that the number 3^1024-1 should be divisible by 24, which in turn means that it shold be divisible by 3But we can see that 3^1024-1 can never be divisible by 3 as it will always leave a remainder of 2 when divided by 3
good observation but I think the question is something like this "What is the highest possible value of 'n' for which 3^1024 – 1 is divisible by 2^n?" kissi zamaane mein AIMCAT mein aaya tha :P
If this is not the case, then my solution is incorrect :)
good observation but I think the question is something like this "What is the highest possible value of 'n' for which 3^1024 – 1 is divisible by 2^n?" kissi zamaane mein AIMCAT mein aaya tha If this is not the case, then my solution is incorrect
good observation but I think the question is something like this "