Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime.
This problem involves a different sense of balance. Consider the input number x to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next m smaller numbers to the left and the next n larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number x is a seesaw number if m and n can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.
For example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right.
Write a function to determine whether the input number is a seesaw number.
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