Problematics | How to use candles as your timekeeper

Jun 26, 2023 04:10 PM IST

The line between a textbook sum and a ‘puzzle’ is not always clear. Here’s an example that may straddle both words.

Suppose one of my puzzles went thus: “A car on a highway covers 320 km in 4 hours. At the same average speed, what distance would it cover in the fifth hour?” You would have reacted with outrage at this exercise, which belongs more to a school textbook than a puzzles column.

Welcome to Problematics!(Shutterstock) PREMIUM
Welcome to Problematics!(Shutterstock)

That said, I have never been sure about the dividing line between a textbook sum and a thinking person’s puzzle. Some examples appear to straddle both worlds, such as the one below.

#Puzzle 44.1
#Puzzle 44.1

At 12:30 am, her eyes straining, she lights the second candle, too, and continues studying under the combined light.

At 8 am, the drowsy student notices that the two candles are now exactly the same length. She falls asleep without blowing them out.

In the afternoon, she wakes up to find that the shorter candle has burnt out while the longer one is on its last legs. The end comes at 2 pm.

Had she been awake, she would have noticed the shorter candle’s end too — at 12:30 pm.

What were the lengths of the two candles before she lit them?

#Puzzle 44.2

#Puzzle 44.2
#Puzzle 44.2

If the opponent responds with 1 to FLICK, her word would include T, R, E, A, I. As such, only one can be formed under the rules – IRATE.

— Meher Sandhu, Gurgaon

TAWER is a noun that derives from the verb TAW, which the Chambers English Dictionary defines as “to prepare and dress (skins) to make leather, using an alum and salt solution rather than tannin”. Thanks for the new word, Meher.

#Puzzle 43.2

#Puzzle 43.2
#Puzzle 43.2

Solved #Puzzle 43.1: Sara Khanna (Fremont, California), Ruchir Kohli (Delhi), Nathan Sequeira (Mumbai), Anil Khanna (Ghaziabad), Geetansha Gera (Faridabad), Siddharth Oswal (Ludhiana), Yash Singla (Panipat), Mayobhav Pathak (Gurgaon), Namrata Raina (Ghaziabad), Subrata Chakravorty (Gurgaon), Lokesh Mittal (Sadabad), Sunil Kumar Raina, Shilpa Negi, Kshitij Kumar, Akshaya Paul, Mudit Singhal, Kiran Chandranna, Sri Ramachandra Sai, Akshay Khanna

Solved #Puzzle 43.2: Rohit Khanna (Noida), Amar Lal Miglani (Mohali)

Problematics will be back next week. Please send in your replies by Friday noon to

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    Puzzles Editor Kabir Firaque is the author of the weekly column Problematics. A journalist for three decades, he also writes about science and mathematics.

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