![]() ![]() That gives us this result, where someone says that the formula is 2^(N+1)-1 and that this is in fact a geometric series, and then we lose like three hours on Wikipedia but that's okay. Since we need to take the sum of those things, and we can tell by looking at them that they're powers of two, we stick " sum of powers of 2" into the ALL KNOWING ORACLE. Now, if we factor out 20 units of food from those numbers (it's 5 * 4, which are just constants we've applied), we get a simple pattern: level 1 requires 1, level 2 requires 2, level 3 requires 4, level 4 requires 8, and so on if we can figure out a quick way to sum that up from level 1 to level 15, (or alternatively, from 2^0 to 2^14) then we just need to multiply everything by 20 and we'll have our answer. You need to feed a dragon four times before it levels, so we can factor that in and pretend it's already required - a level 1 dragon requires 5 * 4 = 20 units of food to level, a level 2 dragon requires 40, a level 3 dragon requires 80, and so on. Every level after that, the amount of food doubles - level 2 requires 10 food, level 3 requires 20 food, etc. Dragons start off at level 1, needing to be fed 5 units of food at a time. ![]()
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