The HERO System is a role-playing game system designed to allow players to play superheroes. In the system, each character is given a point value, and he can use the points to buy powers, abilities, and stats. For the purposes of this problem, there are two powers that are important:
Followers - This power allows a character to have other characters as allies. The player can select the number of allies as well as the point value of those allies. The point cost of this power is computed as follows:
- 1/5 of the point value of the ally characters. For example, a 50-point ally costs 10 points.
- If the ally has a point value exceeding that of the original character, an additional cost equal to the difference in points. For example, if a 100-point character has a 150-point follower, that costs the character 80 points (30 points for 1/5 of the cost, plus an additional 50 points)
- If there is more than one ally, a 5 point increase for each doubling of the number of allies. For instance, two 50-point allies costs 15 points, four 50-point allies costs 20 points, eight 50-point allies cost 25 points, etc.
Duplicates - This power allows a character to make multiple copies of himself. The cost of this power is 1/5 of the point value of the character for a single duplicate, and a 5 point increase for each doubling of the number of duplicates. For example, a 100-point character would pay 20 points for one duplicate, 25 points for two duplicates, 30 points for four duplicates, etc.
Duplicates may not have their own Followers or Duplicates.
Now the question: What is the maximum number of "units" (counting the original character and any Followers and Duplicates) that a 100-point character can field?
Here is the solution.