Games children play. From around the world, games like mancala and tangram in a new exhibit

ACROSS thousands of miles and hundreds of years, children's games have made a passage to the tiny Children's Museum of Manhattan. On one wall of the museum, you'll find Go Bang, dating from 2000 BC. On the floor are blue, star-shaped hopching tables from China. Wooden tables shaped like narrow, fanciful little animals are provided for playing mancala - ``the oldest game known to man,'' according to Kirk Tolchin, coordinator of the museum's exhibition on children's games, which runs through the end of March.

Displayed as art, in glass cases on the walls, are curious antique games, the sort of thing that would have been played in the bosom of a large Victorian family, things like The Wall Street Game, with an oddly anti-capitalist cover featuring a bear and a bull, in coats, ties, and monocles, shearing a sheep; Chiromagica, a pretty easy form of Trivial Pursuit; and Traps, a kind of bowling with marbles.

Shirley Roemer and her five-year-old son, Jonathan, were playing tick-tack-toe. Mrs. Roemer said that Jonathan prefers familiar games, but she had been trying to expand his horizons to include tiddlywinks. ``I got 25 points,'' Jonathan remarked, unsolicited.

The games are placed in appropriate environments; the tangram puzzles, for instance, are under a red pagoda painted on the wall representing China. ``They come into the environment and they can experience what it might be like to be in China...,'' Mr. Tolchin explains.

Tangram puzzles are exquisite and very Chinese and not for those who have trouble putting the truck-shaped piece in the hole next to the word ``truck.'' It consists of small wooden pieces in different shapes that you make elegant pictures with; the museum provides a drawing of the design, but the artistic part is figuring out which pieces to use to make it.

``This is the running man,'' said Tolchin, quickly finishing one. ``Children use them to problem-solve. It's a puzzle that has endless possibilities.''

We moved over to where a plastic palm set in yellow cement sand represented Africa. In the sand were two rows of six holes with small black markers in them: the most primitive form of the game mancala.

``It can be played simply with beans. We've taught children to do it with egg cartons,'' Tolchin said, pointing to a pile of egg cartons, which very conveniently have two rows of six holes.

Many games are traditionally male and female, says Tolchin.

``A lot of girls know hopscotch and boys don't. But if you look at hopscotch in Italy or India, you'll see boys playing it.

``Games have vogues like everything else - for instance, hopscotch is not as popular as it was 20 years ago. A lot of kids haven't seen marbles; the parent comes in and says, `Oh, marbles - what a great game.'

``Tiddlywinks is an 18th-century game. And the fishpond [a box with magnetized fish that you catch on a hook] - that's an 18th-century idea. Chess is an Indian game played by the Indian generals. Checkers was like a parlor game in France for the elite.''

This exalted origin did not affect two little boys who were at that moment using the giant checker set to reinvent shuffleboard.

``That's pretty common,'' says Tolchin. ``It's OK to use games in a different way. Making up your own rules is what games are all about.''

Some people, however, don't like it when you make up your own rules. A bearded man and his little son were playing hopching.

``No, that's not one space; you have to work your way up one space only,'' said the father.

The little boy had a different idea; he started playing a game of his own invention called ``I'm bored.'' The object of this game is to keep any adults in the vicinity on the hop. It is always in the power of parents to checkmate, however, and father and son headed out the door.