Burt Kaliski Jr. (@modulomathy)
3/29/12 7:10 PM
#math trivia for #March29: #89 can be constructed from the numbers 8 and 9 with + and * operations. How? What if you also had – and / ?
With just addition and multiplication, the simplest construction is 89 = 8*9 + 8 + 9. A longer form is possible by adding multiple 8s and 9s.
With subtraction, it’s possible to compute a 1, and given a 1, it’s possible to compute any integer. Division may give some shortcuts, but to get to 89 with division, you’d need to get something larger first, so overall it would probably take more steps.
I didn’t write down any shortcuts when I posted the problem, so if there was something that – and / helped with, I may have forgotten …