In which Brain teaches Pinky his numbers
Brain begins Pinky's first math lesson by writing "1" on the blackboard, asking "Pinky, do you know what this is?" Pinky responds, "YEP! It's one one!" Brain slaps himself on the forehead. "No Pinky, 'one one' is like this," he writes "11" on the board. "And it's called eleven." Pinky looks confused, "But that's two one..." he says. Brain writes "21" on the board, but before he can speak, Pinky continues, "And that's one two and one one." So Brain writes "1211." Pinky cuts in, "...and that's one one, one two, and two one!" Brain writes "111221"...
If the conversation and blackboard work continues in this fashion, in what number will Brain write the first 4?
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1 solution
This is the Conway suite. Basically, you can't have a 4 because that would mean four identical numbers in the previous line, like 1111, 2222... But this is impossible. http://eljjdx.canalblog.com/archives/2015/06/29/32278826.html