4
1 5 3
1 5 1
1 5 10
7 7 7
3
1
0
You are given three integers lll, rrr, and xxx.
Count the number of pairs (a,b)(a,b)(a,b) such that l≤a≤b≤rl \le a \le b \le rl≤a≤b≤r and the arithmetic mean of aaa and bbb is equal to xxx, i.e. a+b2=x\frac{a+b}{2} = x2a+b=x.
l=1l=1l=1, r=5r=5r=5, x=3x=3x=3
We need pairs (a,b)(a,b)(a,b) with 1≤a≤b≤51 \le a \le b \le 51≤a≤b≤5 and a+b2=3\frac{a+b}{2}=32a+b=3, i.e., a+b=6a+b=6a+b=6. Valid pairs: (1,5),(2,4),(3,3)(1,5), (2,4), (3,3)(1,5),(2,4),(3,3). Answer: 3.
l=1l=1l=1, r=5r=5r=5, x=1x=1x=1
We need a+b=2a+b=2a+b=2 with 1≤a≤b≤51 \le a \le b \le 51≤a≤b≤5. Only valid pair: (1,1)(1,1)(1,1). Answer: 1.