Sixty-Third Journal Entry

[puzzledprof]

[Backdated to Saturday]

Ah, I was petting Claire earlier, and she reminded me of a puzzle I know.

If 0 + 1 = dog, 0 + 2 = cat, 6 + 3 = dog, 6 + 7 = dog dog, 7 + 9 = dog cat, 11 + 12 = cat dog, and 11 + 17 = cat cat, then what is the smallest number you can add to 1 to get dog dog dog?

Comments

[dustedsunlight]

Uhm...well if dog is one, then you need three ones, for 111. So you'd have to add 110, right?

[puzzledprof]

The answer is correct, but that's not why. One is merely one of the numbers "dog" can be.

[dustedsunlight]

Oh, okay... uhm, well, 6+3 is 9, which is another dog, and 6+7 is 13, which is dog dog...

Aah, I'm confused. I'm not really good with math puzzles. I guess you could subtract cats or something, if you needed to use the other ones... like, if cat dog is 22, then if cat dog minus cat is 22-2 is 20... ooh, I feel like I'm tying myself in knots.

[puzzledprof]

I'll give you a hint; every single whole number can be put into two groups. "Dogs" represent one group, "Cats" represent the other.

[dustedsunlight]

Okay, ah...

Is it even and odd numbers? Like, 1 is dog, 2 is cat, 3 is dog, like that. So 11 would be dog dog but 12 would be dog cat. So to get to dog dog dog, you would need 111!

Am I right?

[puzzledprof]

That's correct!

[dustedsunlight]

Yay! These puzzles are a lot of fun.