The river-crossing puzzle

In your book, Maths Mela (Chapter 1), Sanju and Mira are travelling on a train. To pass the time, they give each other puzzles. Mira gives Sanju the river-crossing puzzle.

A boatman has to take a lion, a sheep and a bundle of grass across a river. His boat is small: he can take only one of them at a time. But there are two dangers. If the sheep and the grass are left on a shore without him, the sheep will eat the grass. If the sheep and the lion are left without him, the lion will eat the sheep. The lion does not eat grass, so the lion and the grass are safe together.

The sheep is the trouble-maker: it is in both dangers. So the boatman must take the sheep across FIRST. If he took the lion first, the sheep would eat the grass. If he took the grass first, the lion would eat the sheep.

Here is the clever part. He comes back and takes the lion across. Now the lion and the sheep are together on the far shore, so he brings the sheep BACK with him. He leaves the sheep and takes the grass across; the grass stays safely with the lion. Then he goes back one last time and brings the sheep.

Count the crossings: sheep over (1), back alone (2), lion over (3), sheep back (4), grass over (5), back alone (6), sheep over (7). So it takes 7 crossings. (Taking the grass over at step 3 and the lion at step 5 also works, with the same number of crossings.)