og11 ps #248

[throne]

大家好

#248
right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P,Q, and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed?

ans:9900=10X11X9X10

不懂為什麼乘以9x10?

謝謝!

[dibert8]

PQ = 10, PR = 9, 8, 7, ... , 1; RP = 9, 8, 7, ... , 1 (mirror 左右)
PQ = 9, PR = 9, 8, 7, ... , 1
...
PQ = 1, PR = 9, 8, 7, ... , 1
PQ 也可以 mirror (上下)
=> 2*[(1+10)*10/2]*2*[(1+9)*9/2] = 11*10*10*9 = 9900