The Induction Penguin
A hypothetical penguin used to teach mathematical induction. To show that the penguin can climb arbitarily high on a ladder, it is sufficient to show that 1. it can climb to the first rung, and 2. if it can climb to the X rung, then it can climb to the X+1 rung.
Mathematical Induction
is a mathematical proof technique used to prove a given statement about any well-ordered set. Most commonly, it is used to establish statements for the set of all natural numbers. Basically it is a two step process to prove a given statement about a set of numbers, if the statement is true for one number then it must be true for the next number as well.
Sometimes I make a statement that I cannot prove but I know it is true like, "You only need a parachute if you want to skydive twice". I wouldn't want to test it but I believe it to be true. Fortunately for us we do not need to prove the numbers we come up with, we have a checker to do it for us.
Here is the Puzzle
N 33 31.978 W 082 17.065
N 32 36.907 W 094 50.135
N 26 53.879 W 082 03.551
N 40 01.951 W 074 08.094
N 38 12.529 W 085 44.687
N 30 08.337 W 095 46.613
N 32 40.799 W 096 49.124
N 39 47.380 W 075 29.114
N 38 54.601 W 077 11.433
N 40 05.980 W 074 56.170
N 48 10.690 W 110 17.384
N 36 17.125 W 115 12.059
S 33 31.913 E 138 11.950
N 41 38.664 W 071 27.427
N 36 57.855 W 079 51.284
You can validate your puzzle solution with certitude.