Five towns whose fortunes were made where the water stopped being flat: a horseshoe of green river on a national border, a rainforest crescent of 275 drops, a mile-wide curtain of spray, a 20-metre step on Norway's longest river, and the one ledge on the Mississippi.
The Horseshoe Falls opposite the town is 57 metres high with a crest curving for about 670 metres, and takes roughly 90% of the river's flow. A 1950 treaty halves the flow over the crest overnight, from about 2,800 to 1,400 cubic metres a second, once the tourists have gone and the surplus can run through the power stations.
The falls upriver form the largest waterfall system in the world — a 2.7 km crescent of some 275 drops, the deepest of them the 80-metre Devil's Throat. The Itaipú dam 15 km north supplies the bulk of Paraguay's electricity.
David Livingstone saw the falls on 16 November 1855 and renamed them for Queen Victoria. At 1,708 metres wide and up to 108 metres deep, the sheet of water is reckoned the largest single curtain of falling water on earth — and the town beside it was capital of Northern Rhodesia until Lusaka took over in 1935.
Sarpefossen drops 20.5 metres carrying about 577 cubic metres a second — the last and heaviest fall on the Glomma, Norway's longest river. Olav Haraldsson founded the town beside it in 1016, and the Borregaard biorefinery on the bank is the only plant in the world making vanillin out of wood.
Saint Anthony Falls was the only major natural waterfall on the whole Mississippi, and the mills it turned made this the flour-milling capital of the world from about 1880 to 1930. Its soft limestone lip was eroding upstream so fast that engineers had to cap the falls with a timber apron in 1880, replaced by concrete in 1952.
Think you'd have found them? Play today's expedition, or replay this one from the archive.