In just 1 hour 30 minutes, the New World will say goodbye to 2011 and hello to 2012, and a good way to do this is with generosity.
So, I'm going to give 12 Q6 weapons + 12 Q6 food to the first citizen who can PM me the correct answer to one of the questions below. Since there are 12 questions, then 12 citizens will get a prize. So in total, I will give away 144 Q6 weapons + 144 Q6 food.
But wait, there's more: if a citizen PMs first the correct answer to 3 of the questions, I will give him/her 2012 PHP in addition to his/her 36 Q6 weapons and 36 Q6 food.
So, here are the questions:
Let A be the set of all integers of the form n + (n + 1) + (n + 2) + ... + (n + k), where n, k are positive integers. Suppose the elements are arranged in ascending order, find the 2000th term. Answer: 2011, correctly answered by tster
Find the largest 3-digit number (ABC) such that 14A + 49B + 2C = 263. Answer: 832, correctly answered by DrummerMike
Let p(x) be a polynomial such that its leading coefficient is 1 and 27(x – 1)p(x) = (x – 27)p(3x) for all real numbers x. Find p(4). Answer: 115, correctly answered by DrummerMike again
Let x, y, z be three prime numbers such that xyz = (129)(141)(147) + 320. Answer: 131, 137, 149, correctly answered by DrummerMike for the third time
For any positive integer n, let a(n) be the remainder when 7^n is divided by 100. Find the value of a(1) + a(2) + a(3) ... + a(100). Answer: 2500, correctly answered by DrummerMike for the fourth time
Let f and g be two polynomials such that f(x +g(y)) = 3x + y + 4 for all real numbers x and y. Find the value of g(8 + f(3)). Answer: 7, correctly answered by DrummerMike for the fifth time
7. Suppose a and b are two real numbers satisfying (a – 5)^2 + (b – 5)^2 = 18. Find the largest possible value of a/b.
Let f(x) be a rational function such that f(x) + f((x – 1)/x) = 1 + x for any real number x ≠ 0, 1. Find the value of f(10). Answer: 899/180, correctly answered by vasmegye
Find the largest possible remainder when the square of a prime number is divided by 24. Answer: 9, correctly answered by tster again
Find the positive integer x such that (x^2)/(720 – x) is a prime number. Answer: 45, correctly answered by tster for the third time
Suppose 1ababababab is an 11-digit integer which is divisible by 99. Find a + b. Answer: 16, correctly answered by tster for the fourth time
ABCD is a square-shaped piece of paper of area 81 sq cm. A square of area 1 sq cm with one vertex at A and sides parallel to those of ABCD is removed from ABCD. If the remaining part is cut into k congruent triangles, Answer: 20, correctly answered by tster for the fifth time
what is the smallest possible value of k?
Oh, and don't forget to vote and subscribe.
Note: This will close on Jan. 23, Chinese New Year
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