Harvard- MIT math tournament

<p>While online yesterday, or the day before (i dont exactly remember) i found some interesting problems from an old Guts team round of the math tournament. These problems were i think from march 15 2003.</p>

<p>Here are some sample problems if anyone is interested…</p>

<p>6) compute the surface area of a cube inscribed in a sphere of surface area pi.</p>

<p>14) A positive number will be called sparkly if its smallest (positive) divisor, other than 1, equals the total number of divisors (including 1). How many of the numbers 2,3,4,5…2003 are sparkly</p>

<p>36) A teacher must divide 221 apples evenly among 403 students. What is the minimal number of pieces into which she must cut the apples? (a whole uncut apple counts as a piece)</p>

<p>11) Find the smallest positive integer n such that 1^2+2^2+3^2…+n^2 is divisible by 100. </p>

<p>Theres like 40 problems, and the max number of points is 400. I think the top last year was 210 or something.</p>