guess and check table can be found by linking to this website.
http://home.avvanta.com/~math/guess.html
construct your table as follows:
s 4*s 4*s-23 match 417?
100 400 377 too low
200 800 777 too high
150 600 577 too high
125 500 477 too high
110 440 417 match *********
I started at 100, then doubled it, then halved the difference, then halved the difference again, then took close to one half the distance, lowering my estimate if too high and raising it if too low.
Sears tower is 110 stories high.
Some interesting tidbits regarding tellest buildings in the world.
http://www.infoplease.com/ipa/A0001338.html
Another interesting tidbit from http://en.wikipedia.org/wiki/Willis_Tower
The tower has 108 stories as counted by standard methods, though the building's owners count the main roof as 109 and the mechanical penthouse roof as 110.