Yes, with that I agree. The answer should be one. I think they didn't consider that the number must be positive.

]]>Hi Thurhame

Can you specify where it was claimed that 1+1/(1+1/(1+...)) is equal to 2?

Oh, my mistake, it just said there were two solutions to the formula. However, that's still wrong; my proof shows that any solution must be equal to the golden ratio, i.e. there are at most 1 solutions.

Edited my post above. Thanks!

]]>The answer given is 2 when it should be the golden ratio.

]]>Can you specify where it was claimed that 1+1/(1+1/(1+...)) is equal to 2?

]]>The puzzle claims there are two solutions to "1+(1/(1+(1/...)))". However, it actually converges to the golden ratio , meaning there is only one solution.

MORE COMPLEX PROOF:

The formula is the limit as n goes to infinity of the sequence

Assume some exists (otherwise the sequence would be undefined).

Define a sequence .

We proceed by induction.

Base step:

Inductive Hypothesis:

Thus we have proved by induction the relation for all .

Since is a sequence of the form , this ratio converges to the golden ratio.]]>

GF's usually count the number of solutions not the type of solutions. For that, I usually call on number theory.

Still in all a gf played an important part in the program. Without it there would be no program.

]]>A mathematical solution would be nice but I do not have one.

]]>Funny that Bob and I went for the same problem.

For the weighty problem there are 10 solutions to the problem. Not counting permutations. Want to add the rest? Hope I did not prune out any others.

]]>Sorry ... bit of a rush.

Weighty Puzz think I have another soln.

More later

Bob

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