Search code examples
logicnumberspuzzle

Godel, Escher, Bach Typographical Number Theory (TNT) puzzles and solutions

In chapter 8 of Godel, Escher, Bach by Douglas Hofstader, the reader is challenged to translate these 2 statements into TNT:

"b is a power of 2"

and

"b is a power of 10"

Are following answers correct?:

(Assuming '∃' to mean 'there exists a number'):

∃x:(x.x = b)

i.e. "there exists a number 'x' such that x multiplied x equals b"

If that is correct, then the next one is equally trivial:

∃x:(x.x.x.x.x.x.x.x.x.x = b)

I'm confused because the author indicates that they are tricky and that the second one should take hours to solve; I must have missed something obvious here, but I can't see it!

Solution

  • Your expressions are equivalent to the statements "b is a square number" and "b is the 10th power of a number" respectively. Converting "power of" statements into TNT is considerably trickier.