Ttyjukl

I read a short story in a collection of sci-fi stories a few years ago. It was about a supercomputer on which humanity relied upon to answer difficult questions (much like Isaac Asimov's Multivac). However, the twist at the end of the story was that the computer had no computing powers at all, but was really only controlled by a man living inside. I believe the name of the supercomputer was Maize.

Appointment in Tomorrow by Fritz Leiber. It can be found on gutenberg.org.

Two factions compete for power in a post nuclear world: Thinkers
(scientist) have had a lot of power and popularity due to fantastic
inventions (some of those might be only a deception), but there are
opposing forces.

It starts with Jorj Helmuth, a Thinker awaking up and being informed that the President and his general staff are waiting to see Maizie:

Huge as a primitive nuclear reactor, the great electronic brain loomed
above the knot of hush-voiced men. It almost filled a two-story room
in the Thinkers' Foundation. Its front was an orderly expanse of
controls, indicators, telltales, and terminals, the upper ones reached
by a chair on a boom.

Although, as far as anyone knew, it could sense only the information
and questions fed into it on a tape, the human visitors could not
resist the impulse to talk in whispers and glance uneasily at the
great cryptic cube. After all, it had lately taken to moving some of
its own controls--the permissible ones--and could doubtless improvise
a hearing apparatus if it wanted to.

For this was the thinking machine beside which the Marks and Eniacs
and Maniacs and Maddidas and Minervas and Mimirs were less than
Morons. This was the machine with a million times as many synapses as
the human brain, the machine that remembered by cutting delicate
notches in the rims of molecules (instead of kindergarten
paper-punching or the Coney Island shimmying of columns of mercury).
This was the machine that had given instructions on building the last
three-quarters of itself. This was the goal, perhaps, toward which
fallible human reasoning and biased human judgment and feeble human
ambition had evolved.

This was the machine that really thought--a million-plus!

This was the machine that the timid cyberneticists and stuffy
professional scientists had said could not be built. Yet this was the
machine that the Thinkers, with characteristic Yankee push, had
built. And nicknamed, with characteristic Yankee irreverence and
girl-fondness, "Maizie."

...

Meanwhile the question tape, like a New Year's streamer tossed out a
high window into the night, sped on its dark way along spinning
rollers. Curling with an intricate aimlessness curiously like that of
such a streamer, it tantalized the silvery fingers of a thousand
relays, saucily evaded the glances of ten thousand electric eyes,
impishly darted down a narrow black alleyway of memory banks, and,
reaching the center of the cube, suddenly emerged into a small room
where a suave fat man in shorts sat drinking beer. ... For many
minutes the only sounds were the rustle of the paper ribbon and the
click of the taper, except for the seconds the fat man took to close
his eyes, or to drink or pour beer. Once, too, he lifted a phone,
asked a concise question, waited half a minute, listened to an answer,
then went back to the grind.

Until he came to Section Five, Question Four. That time he did his
thinking with his eyes open.

The question was: "Does Maizie stand for Maelzel?"

He sat for a while slowly scratching his thigh. His loose, persuasive
lips tightened, without closing, into the shape of a snarl.

Suddenly he began to tape again.

"Maizie does not stand for Maelzel. Maizie stands for amazing,
humorously given the form of a girl's name. Section Six, Answer One...