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counting and probability senior
Problem
Joy has thin rods, one each of every integer length from through . She places the rods with lengths , , and on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
(A)
(B)
(C)
(D)
Solution
The quadrilateral cannot be a straight line. Thus, the fourth side must be longer than and shorter than . This means Joy can use the possible integer rod lengths that fall into . However, she has already used the rods of length cm and cm so the answer is
Final answer
B