Challenge of the Week: The Diwali Bridge Dash Before the Torch Dies

It is the night of Diwali, the diyas are flickering out, and the Sharma family is hurrying home from the mela. Between them and a hot plate of pakoras lies one old, creaky wooden bridge across a dark canal — and a single phone whose torch has just 18 minutes of battery left. Cross too slowly and they'll be stranded in pitch darkness. Can all four make it? Grab a chai, set your own timer, and see if you can plan their crossing before the battery (and the clock) runs out.

The Challenge

Four members of the Sharma family must cross the narrow bridge at night. They have only one phone torch, and the bridge is so rickety that at most two people can be on it at any time.

Because it is dark, anyone crossing must carry the torch — nobody can cross without it. When two people cross together, they must walk at the pace of the slower of the two. The torch cannot be thrown back across; someone has to physically carry it back each time.

Each person walks at a different fixed pace. The time each takes to cross the bridge alone is:

• Chintu (the youngest): 1 minute
• Bablu: 2 minutes
• Uncle: 7 minutes
• Dadi (grandmother): 10 minutes

The torch battery will last exactly 18 minutes. What is the shortest total time in which all four can get safely across? (And therefore — do they make it?)

Hint

The obvious plan is to let the fastest person (Chintu) ferry everyone across one by one. Try it and add up the time — you'll find it's too slow. The trick is to stop wasting your fastest walkers on the return trips and instead send the two slowest people across together, so their large times overlap into a single trip.

Solution

The key insight: the two slow walkers (Uncle, 7 min, and Dadi, 10 min) are the real cost. If you can make them cross at the same time, you only "pay" 10 minutes once instead of 7 + 10 = 17 minutes separately. To set that up, the two fastest people act as torch-bearers on the return trips.

Here is the optimal plan, step by step:

1. Chintu (1) and Bablu (2) cross together. They walk at the slower pace, so this takes 2 minutes. (Running total: 2 min.) Now Chintu and Bablu are on the far side.
2. Chintu (1) returns with the torch. This takes 1 minute. (Running total: 3 min.) Chintu is back on the start side, holding the torch.
3. Uncle (7) and Dadi (10) cross together. They move at Dadi's pace, taking 10 minutes — but this single trip carries both slow walkers across at once. (Running total: 13 min.) Uncle and Dadi are now safely across, joining Bablu.
4. Bablu (2) returns with the torch. This takes 2 minutes. (Running total: 15 min.) Bablu carries the torch back to Chintu.
5. Chintu (1) and Bablu (2) cross together one final time. This takes 2 minutes. (Running total: 17 min.)

Adding it up: 2 + 1 + 10 + 2 + 2 = 17 minutes.

Since the torch lasts 18 minutes, the family crosses with a nail-biting one minute to spare — the screen goes dark just as Dadi steps onto solid ground.

Why can't they do better? The naive "Chintu ferries everyone" approach gives 2 (Chintu+Bablu) wait — let's check it directly: Chintu shuttling Dadi, Uncle and Bablu across one at a time costs 10 + 1 + 7 + 1 + 2 = 21 minutes, well over budget. The reason our plan wins is that it pairs the two slowest walkers into one shared 10-minute trip, and pays only the cheap fast walkers (1 and 2 minutes) for the two necessary return journeys. Any plan that sends a slow walker back, or splits Uncle and Dadi into separate crossings, ends up slower. So 17 minutes is provably the minimum.

Answer: 17 minutes — yes, the Sharmas make it across, with one minute of battery left.