Art in new dimensions: The Weekly Puzzle by Dilip D’Souza

The famous painter Vinay Vango had just made a sale

The famous painter Vinay Vango had just made a sale. On a 5 ft by 7 ft canvas, the biggest he had ever used, he depicted the climactic moment of India’s victory over Australia in the Brisbane cricket Test. A cricket-lover in distant Jalpaiguri bought it as soon as he put it up for sale on his website.

All of Vango’s previous sales had been to customers within Mumbai. This was the first time he’d have to ship one to another city. The freight company he consulted was willing to take it to Jalpaiguri. However, their regulations specified that the linear dimensions — length, breadth and height — of any box or crate they carried could not exceed 3 ft.

Dismayed, Vango mentioned his dilemma to his colleague Prabhat Peekachu, who asked: “Can you roll it up?”

“I can,” said Vango.

“Then roll it up and crate it!” said Peekachu.

And that’s what Vango did, and was able to dispatch the painting to Jalpaiguri, meeting the freight company’s size specs.

Question: How?

Bonus: Can you think of why this may not work?

Scroll down for the answers.

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Answer

Vango built a crate in the form of a 3ft by 3 ft by 3ft cube. He rolled up the painting so that it formed a 5ft long shaft. This he fit neatly into the crate, from one corner to the opposite corner. A week later, he got a happy call from Jalpaiguri.

Why did this work? In any given cube, the length of that particular diagonal is the length of its side times the square root of 3. The square root of 3 is about 1.7. Thus a 3 x 3 x 3 crate has a diagonal about 5.1 ft (3 x 1.7): 0.1 ft longer than, and thus just enough for, Vango’s rolled-up painting.

Why the square root of 3? Apply the Pythagoras theorem twice. The first time, to the bottom face (say) of the crate (3 ft length by 3 ft breadth), to find that its diagonal is 3 times the square root of 2. The second time, with that diagonal and the 3 ft height of the crate, to find that the diagonal in question is 3 times the square root of 3 ft long, or about 5.1.

Bonus: We are counting on Vango’s rolled-up painting not being especially thick. After all, we have just 0.1 ft — just over an inch — to play with. It’s possible that the rolled-up shaft, while certainly no more than 5 ft long, will be so thick that the crate will not shut.