Date: Sun, 5 Oct 1997 01:18:06 -0400

From: Alex Bogomolny

Oh, boy.

(23)_{b} means 2b + 3 and (111)_{b} = b^{2} + b + 1.
So your first problem is the same as

5b + 6 = b^{2} + b + 1.

Solve b^{2} - 4b - 5 = 0 to get b_{1} = 5 and
b_{2} = -1. Hence, the answer is b = 5.

Since 2*1/2 = 1 in all bases, 1/2 is one and the same thing in all bases. With this hint, can you do [B] now? The answer is b = 7.

Good luck,

Alexander Bogomolny