## Problem Statement

This problem asked what number of moves it took to kill 5 switches. But there were very specific rules. You could just switch a switch if the change directly to the left was on and each other switch to one side was off. The change most remote to one side didn't make a difference and could be switcher paying little respect to what position the greater part of alternate switches were in. At that point it asks what number of moves it would take to kill 10 changes lastly to demonstrate any equation or example I have thought of.

## Process

To start with I began small, I began with 2 switches and what number of moves it would take to turn every one of them off, then I proceeded onward to 3 and 4 until I achieved 5. When I had done each of the 4, I made a x and y table to attempt to see an example. I saw that 3 switches required 3 moves more than 2 switches, then that 4 switches required 5 moves more than 3 switches lastly 5 switches required 11 moves more than 4 switches. At first I thought it would increment by odd numbers which would make 6 switches require 13 moves more than 5 switches, however that hypothesis didn't work out subsequent to the base number of moves for 6 switches was 42. At that point I saw that at times it was multiplying the quantity of moves before and at times it was one more than twofold of what was some time recently. I utilized this example to make sense of what number of moves it would take to kill 10 switches.

## Solution

The minimum number of moves required to turn off 5 switches is 21. The minimum number of moves required for 2 switches is 2, for 3 it’s 5, for 4 it’s 10. I couldn’t find a general formula for all cases, only found separate formulas for odd number or even number of switches. For odd numbered switches, you double the number of moves from the number of switches before and add one. For even numbered switches, you simply double the number of moves from the number of switches before.

## Problem Assessment

I enjoyed this issue despite the fact that I couldn't construct a general formula. This helped me to remember the tower of hanoi and a problem we did in Mr. B's class junior year. I don't recollect precisely how it went, but there was a line of 4 individuals taking a seat and you needed to get the last individual to be the one and only standing up yet a man could just move if the individual directly before them was standing up and others before them was taking a seat. Fundamentally the same as the switches. This problem was a good reference because between each move, the principal individual, or in this present issue's case, switch, would move.

## Self Assessment

I think I did sort of good on this problem. I was not able to figure out the general equation yet I think I got quite close. I got innovative without an equation to locate the base number of moves it would take to kill 10 switches without really working it out on the grounds that it would have been a ton of moves. I invested a considerable measure of energy in this problem, attempting to locate the base number of moves since I would dependably get stirred up and botch up. The first occasion when I couldn't discover any examples in my number so I backtracked and attempted again and got a littler number so I checked the majority of my base number of moves.