World Mathematics Invitational:.........Month:..........Year:...........

Total Core =

  • Question 1: If A, B, and C are three distinct positive integers such that 0 < A < B < C and A + B+ C = A x B x C, find C - A + B.
  • Question 2: Use 27 small wooden cubes to pile up into a large cube and paint the surface of the large cube with red paint. If these small cubes are separated, total how many faces of those small cubes have no paint on them?
  • Question 3: Use match sticks to arrange the following figures. For example, Figure 4 has 16 small equilateral triangles.
    How many match sticks are required to arrange for 36 small equilateral triangles?
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  • Question 4: The figure on the right shows an addition in which each type of English letter represents distinct digit.
    If it is known that W = 7 and I is an even number, what does M represent?
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  • Question 5: Let A, B, and C be distinct single decimal digits.
    Lois is participating in an event in which she has to run a distance of AC (a two–digit number) kilometers.
    She starts from a location marker that indicates the starting point to be at the BB kilometer mark.
    When she arrives at the finish line, the location marker labels the AAA (a three–digit number) kilometer mark.
    How many kilometers did Lois run?
  • Question 6: Compute (1 + 2 + 3 + ... + 2014 + 2015 + 2014 + 2013 + ... + 3 + 2 + 1) ÷ 2015.
  • Question 7: An isosceles trapezoid has 55, 25, and 15 as the lengths of its three sides with its lower base being the longest side.
    What is the perimeter of this trapezoid?
  • Question 8: A group of students line up to arrange into a square.
    If this square adds a new row and a new column to form a larger square, 19 more students will be needed.
    How many students are lined up for the new larger square?
  • Question 9: Three years from now, the sum of two brothers' ages will be 27.
    If the younger brother's current age is equal to the difference between their ages, how old is the younger brother now?
  • Question 10: A total of 2015 balls are separated into 3 piles. After the same number of balls are removed from each pile, the second pile still has 14 balls and the remaining number of balls in the first pile is twice as many as those remaining in the third pile. How many balls were in the third pile in the beginning?