U.S. secretaries of state are accustomed to earning their pay as problem solvers or at least hand holders for foreign leaders whose problems seem overwhelming. They are not used to meeting a potentate, as George P. Shultz did earlier this week, who makes no request and seems to have no problems at all.

The leader was Sultan Hassanal Bolkiah, the monarch of one of the world's smallest and richest countries, the newly independent state of Brunei, tucked away on the north corner of the Pacific island of Borneo.

The sultan, who has been described in the Guinness Book of World Records as the richest man in the world, received Shultz in an audience room of his new 1,788-room palace, a splendorous edifice of gold, marble and teak which, in contrast to the country's diminutive size, is said to be the largest royal palace on earth.

The whirlwind visit on Tuesday by Shultz, the highest ranking American to come here, was seen by U.S. officials as a step toward diversifying Brunei's international connections. Brunei was a British protectorate for nearly a century until its independence 2 1/2 years ago. Its oil resources were developed by a British-Dutch oil firm.

Brunei, which pumps about a barrel of oil per day for each of its 220,000 inhabitants, was described by a U.S. official as a country with "no significant problems of any kind." There is free medical care for every citizen, free education through the university level, no income tax, few import duties and heavily subsidized housing and automobiles for government employes, who make up more than half the Bruneian work force.

The per capita annual income of Bruneians is said to be close to $20,000, but there is no doubt from the rustic look of some rickety housing (despite the Mercedes parked outside) that there are substantial social and economic differences in the population.

There also can be no question, given the staggering opulence of the sultan's life, that there is a great difference between the royal palace and the rest of the country. No dissent has been reported, however, and there is little that passes for political activity in this country of close-knit ties and Islamic tradition.

People along the steamy streets of the capital peered up in surprise at Shultz's motorcade of a dozen vehicles.

Brunei takes in so much more money than it spends that its official foreign exchange reserves are estimated to be about $20 billion, just short of the $27 billion reported to be held by Japan, the world's second-ranking economic power.

There is no available estimate of the sultan's personal wealth, but it is generally believed to be as monumental as his palace. Bolkiah, who likes polo, helicopters and fast cars, is reported to be the behind-the-scenes owner of the Dorchester Hotel and possibly Harrods department store in London.

The sultan, who is 39, had no requests to make of Shultz in their 50-minute meeting, which was the central feature of Shultz's three-hour stopover en route from Singapore to Manila as part of an eight-day Asian swing. The U.S. secretary of state, in turn, made no requests of Bolkiah, according to Shultz's aides.

Afterwards, Shultz called the meeting "a very fine visit" which strengthened U.S.-Brunei relations. Brunei is squarely in the western camp in global politics, with no diplomatic relations with any member of the Soviet Bloc or China.

Shultz said it was "a real treat" to take a tour of such palatial wonders as the throne room, which is about the size of a football field, can seat 2,000, and has only been used once. The Bechtel Corp., which Shultz formerly headed, was a major contractor on the palace.

Shultz also visited the U.S. Embassy in Brunei, made a short pep talk there and posed for a picture with the entire staff. The embassy, among the smallest the United States operates in the world, is headed by Barrington King, a career officer, and has six American employes