This is an interesting problem from the book Speed Baduk Level 10. I am uncertain if the given answer is correct. I found a variation which gives white a ko, which seems better than the solution.I'd appreciate any comments on this. Here's the SGF:
[sgf-full](;CA[hz-gb-2312]AB[rn][rr][rq]AW[ro][so][qp][qq][qr]AP[MultiGo:4.4.4]SZ[19]AB[rp]
MULTIGOGM[1]
;B[qo];W[qn];B[po];W[rm];B[pn]
(;W[qm];B[rs];W[sp];B[pr];W[pq];B[oq];W[or];B[qs];W[ps];B[pp];W[pr];B[nr]C[This is the book's solution.])
(;W[rs]C[But what if white plays here instead?];B[qm];W[sn]
(;B[sp];W[qn]C[Ko for life.])
(;B[rl];W[qn];B[sl];W[sr];B[sm];W[sq];B[rn];W[sp]C[White lives outright.])
(;B[qn];W[rl];B[sm];W[sl];B[sp];W[sm];B[qk]C[Not enough liberties.])))[/sgf-full]

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

Pretty sure the correct answer is:

Please address my variations when you post.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War

(I promise, someday I'll learn to do the diagram thing...)

Starting from your middle variation where black plays r7:

b-r7
w-t6
b-s8
w-r6 (capture)
b-t2
w-r1
b-s6 (capture)

Now, can white ever win the ko? Black can answer every ko threat; what can white do? That's what I see -- never too sure about these things.

Yes, your variation does lead to a ko. However, if the name of the game is to find the best variation, then after S1 from the book variation would White really play T4? Course not, he would probably play something like O3 and let Black live in tiny gote which I think is even better than ko.

The book solution is not the best play for both sides; rather it's the most educational variation, the variation that shows the beautiful squeeze tesuji at the bottom which was the hidden intent behind the problem. Think of R7 (and T4) as "what-if" moves rather than the best moves that pushes the player's reading to the limit. Your move is the better move, but the one shown in the book is the most educational. I don't know how the solutions look in the book, but ideally it should contain all of these important variations rather than just one line.

I did? Black plays S1 before the atari so white can't go there..

Thanks that makes sense. The book indicated that the goal was to save the three black stones in the corner, and that is why I questioned if there was some mistake. It only gave the main variation as the solution.You're of course right about it being better to escape and let black live.

Sorry I didn't see the relation. I don't think that that changes things much though...after white ataris the sequence T17 N17 O19 Q19 O17 turns out pretty much the same.

_________________
"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War