magic.py

def next(life, power, counters):
	for _ in range(1):
		life += 2 * power
		counters += 2 * power
		power = life + counters
	return life, power, counters

def power_at(turn, life, power, counters):
	return 5 ** turn * (life + power + 4 * counters) * 2 // 7

def life_at(turn, life, power, counters):
	return (power_at(turn, life, power, counters) + life - counters) // 2

def counters_at(turn, life, power, counters):
	return (power_at(turn, life, power, counters) - life + counters) // 2

life, power, counters = 1, 2, 1
TURNS = 10

print("{:<7}{:<15}{:<15}{:<15}".format("Turn", "Life", "Power", "Counters"))
for turn in range(1, TURNS + 1):
	life, power, counters = next(life, power, counters)
	
	assert(life == life_at(turn, 1, 2, 1))
	assert(power == power_at(turn, 1, 2, 1))
	assert(counters == counters_at(turn, 1, 2, 1))

	print("{turn:<7}{life:<15} {power:<15} {counters:<15}".format(**vars()))