in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 38500 . how many times did he participate in the competition ?
import math
n0 = 11.0
n1 = 7.0
n2 = 5.0
n3 = 2.0
n4 = 38500.0
t0 = n0 * n1
t1 = n2 * t0
t2 = n3 * t1
t3 = n4 / t2
t4 = math.sqrt(max(0, t3))
answer = math.floor(t4)
print(answer)