I don’t think there’s any place other than math where you can learn how unbelievably creative you get to be in a purely deductive setting. Here are two of my favorite examples:
100 ants crawl left or right on a meter stick at 1 cm/s. When two ants meet, they bounce and both change directions. Ants fall off when they reach the ends. Show that regardless of the starting distribution of ants and directions, they all fall off the stick by the end of 100 seconds. Solution: vaqvivqhny vqragvgl vf na vyyhfvba.
A regular hexagon with side length n is tiled with diamonds of side length 1 (a diamond is two equilateral triangles glued along a side.) Show that there will always be the same number of diamonds in each of the three possible orientations. Solution: gur Neg bs Ceboyrz Fbyivat ybtb.
I don’t think there’s any place other than math where you can learn how unbelievably creative you get to be in a purely deductive setting. Here are two of my favorite examples:
100 ants crawl left or right on a meter stick at 1 cm/s. When two ants meet, they bounce and both change directions. Ants fall off when they reach the ends. Show that regardless of the starting distribution of ants and directions, they all fall off the stick by the end of 100 seconds. Solution: vaqvivqhny vqragvgl vf na vyyhfvba.
A regular hexagon with side length n is tiled with diamonds of side length 1 (a diamond is two equilateral triangles glued along a side.) Show that there will always be the same number of diamonds in each of the three possible orientations. Solution: gur Neg bs Ceboyrz Fbyivat ybtb.