I should also note that the above formula only covers the case where the player hacks the Machines before the first use. The precise effect of hacking is to set the

*second difference* of the cost to 16 instead of 20.

That is, there is a variable, let's call it D1, that starts at 20 and increases by 20 with each use. The first use costs 20; the second costs 20+D1 = 40, and D1 increases to 40. The third use costs 40+D1 = 80, and D1 increases to 60. The fourth use costs 140, and so on. After hacking, the first use still costs 20, and the second still costs 20+D1 = 40, but D1 only increases to 36, so the third use costs 76, and so on.

It follows that if you hack the Machines at any time, the effect will only be noticeable from the third use after hacking.

Working out a formula for the cost of the

*n*th use if you already used the Machines

*m* times before hacking is left as an exercise for the reader

____________________________

50th Skywatcher