Crossing The River In Minimum Time

Four people need to cross a dark river at night. They have only one torch and the river is too risky to cross without the torch. If all people cross simultaneously then torch light won't be sufficient. Speed of each person of crossing the river is different. Cross time for each person is 1 min, 2 mins, 7 mins and 10 mins. 

However 2 can cross together but there is one limitation.If two are crossing the river then it takes time equal to slowest person would take alone. For example, if persons with cross times 1 min & 10 mins are crossing then it would take 10 mins for both to cross the river.

What is the shortest time needed for all four of them to cross the river ? 

  
Find here the efficient way! 

Source 

Efficient Way To Cross The River

What's the challenge? 

Let's name each person by their crossing times as 1,2,7,10.

The instant solution that everyone can think of is using 1 as a usher to guide all. That means 10 & 1 goes, 1 comes back; 7 & 1 goes again 1 comes back and 2& 1 goes finally. This would take 10 + 1 + 7 + 1 + 2 = 21 mins to cross rivers.

Is it really efficient solution? What if we find a way to cross both 10 & 7 in one go & other 1 waiting across to bring back torch.

1. The 1 & 2 goes across but 1 comes back - 2 + 1 = 3 mins required.

2. Now 10 & 7 goes across & send 2 back with torch - 10 + 2 = 12 mins required.

3. Finally after coming back 2 & take 1 across the river - 2 minutes required.

So total 3 + 12 + 2 = 17 minutes required to cross the river for those 4 persons. In first step, 2 can also come back & send 10 & 7. In that case, in second step, 1 has to come back to take 2 across the river. Isn't this a more practical solution?