Challenge of the Week: The Baraat and the Bamboo Bridge

The shehnai has started, the priest is glancing at his watch, and the muhurat will not wait. But four members of the baraat are stuck on the wrong side of a swollen monsoon stream, with only a rickety bamboo bridge between them and the wedding mandap. There is one small problem — make that two. The bridge is so frail it can hold at most two people at a time, and it is pitch dark. There is exactly one hurricane lantern, and nobody dares step onto those slippery bamboo slats without it. Can you choreograph the crossing so the whole party reaches the other side as fast as humanly possible? Solve it before the muhurat slips away.

The Challenge

Four guests must cross the bamboo bridge at night. The rules are strict:

1. At most two people can be on the bridge at any time.
2. Anyone crossing must carry the single lantern — there is no other light, and the bridge cannot be crossed in the dark.
3. The lantern cannot be thrown or slid back; someone must physically walk it back.
4. When two people cross together, they move at the slower person's pace.

The four guests need different times to cross the bridge one way:

• Dadi (grandmother): 10 minutes
• Chacha (uncle): 5 minutes
• The bride's friend: 2 minutes
• The young cousin: 1 minute

What is the minimum total time needed to get all four safely across?

Hint

The obvious plan — let the fastest person ferry the lantern back each time — is not the best one. The real saving comes from sending your two slowest people across together, so their times overlap instead of adding up. The trick is arranging for the lantern to already be waiting for them on the start side when they go.

Solution

Let us label them by their times: 1, 2, 5 and 10.

A tempting first instinct is to make the cousin (1) escort everyone, shuttling back each time. That gives 2 + 1 + 5 + 1 + 10 = 19 minutes — good, but not optimal. The smarter idea is to pair the two slowest people (5 and 10) so that the 5-minute walk is "absorbed" inside the 10-minute one. Here is the winning sequence:

1. Cousin (1) and Friend (2) cross together. They move at the slower pace, 2 minutes. (Time used: 2)
2. Cousin (1) returns with the lantern. (+1 → total 3)
3. Dadi (10) and Chacha (5) cross together. They go at the slower pace, 10 minutes — and crucially, Chacha's 5 minutes happen during this same trip, costing nothing extra. (+10 → total 13)
4. Friend (2) returns with the lantern (she was already waiting on the far side from step 1). (+2 → total 15)
5. Cousin (1) and Friend (2) cross together one last time, at 2 minutes. (+2 → total 17)

Everyone is now across, the lantern has made the journey, and the bridge never held more than two people at once. Add it up: 2 + 1 + 10 + 2 + 2 = 17 minutes.

Why can't we do better? The two big numbers, 5 and 10, must each cross at least once. If they cross separately, their times (5 and 10) add up to 15 just for them, plus the lantern returns — that lands you at 19. The only way to dodge the 5 entirely is to send 5 and 10 together, and the elegant bookkeeping above lets a fast pair (1 and 2) handle every lantern return cheaply. No arrangement beats 17.

The baraat sweeps into the mandap with seconds to spare, the shehnai swells, and the priest finally relaxes.

Answer: 17 minutes.