Problematics | Go with or against the flow and keep it simple

Here's a puzzle that's not as difficult as it may seem. Can you solve it with calculations on relative velocity? Or is there a simpler way?

Sometimes, a seemingly complex mathematical puzzle can be solved in seconds with no more than a little reasoning. For example, the puzzle about milk and water last week. Some readers have used mathematics to solve it correctly, many others have got it wrong, and only a few have used the easier approach — logic rather than mathematics — to arrive at a quick solution.

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There are many other puzzles that appear more complex than they actually are. In some cases, you may solve the puzzle with reasoning; in others, you may need just a little bit of simple mathematics. Such as the following one. In fact, at first sight, it may appear that there is no way to solve it. And then you hit the eureka moment.

#Puzzle 39.1

#Puzzle 39.1

In a flowing river, you are rowing downstream at a constant rate. Your boat is stacked with sundry items, including a ping-pong ball, meant to be a gift for a child you know.

Along the way, the ping-pong ball drops over the edge and into the river, but you don’t notice that immediately. You row downstream for 3 more minutes before you realise that the ball is missing.

Without losing an instant, you turn back, spot the ping-pong ball at a distance, and row upstream at the same rate as before. To make it clear, “same rate” means your independent speed, not your speed relative to the river. Hence, although you row at the same rate, your actual progress in either direction will depend on the flow of the river.

As you row towards the ball, the ball drifts towards you. Eventually, you pick it up at a point half a kilometer downstream of where it had fallen off.

Almost the same thing happens the following day, with some key differences. It’s a different river this time, and you are rowing upstream, at the same rate as the previous day. Once again, the ping-pong ball falls over, and you realise it 3 minutes later. Turning and rowing downstream, you pick up the ball, again half a km downstream of where it had fallen off.

What are the speeds of the two rivers? If you see a coincidence, try out the same scenarios with a different set of variables. That may help you hit on the way to keep it simple.

#Puzzle 39.2

At a vegetable market, you need just one pumpkin, and have two choices. In terms of circumference, one pumpkin is 20% larger than the other. In terms of price, the larger one is 50% costlier than the other.

Which is the better bargain?

MAILBOX: LAST WEEK’S PUZZLES

#Puzzle 38.1

Kabir,

There's as much milk in the water glass as there is water in the milk bottle since the total amount of liquid in the glass and the total amount of liquid in the bottle are unchanged. Milk has displaced water in the glass and water has displaced milk in the bottle.

— Shankar Subramanian

#Puzzle 38.2

A number of readers have sent the total number of dates as 215, because they have included three dates (10-10, 25-4 and 20-5) from the year ending with 00. That doesn’t work, because the product in these dates is 100 but the year cannot be represented as 100.

For #Puzzle 38.1, the lists below include not only readers who have used the simple, ideal approach, but also those who have arrived at the right answer mathematically.

Solved both puzzles: Shankar Subramanian, Deviprakash Seksaria (Navi Mumbai), Amardeep Singh (Meerut), Akshay Bakhai (Mumbai), Rajesh Bansal (Noida), Madhuri Patwardhan (Thane), Sandeep Bhateja (Hoshiarpur)

Solved Puzzle #38.1: Kanwarjit Singh (Delhi), Dr Sunita Gupta (Delhi), Mukesh Arora, Dr Nakul Makkar (Noida), Abhishek Garg (Chandigarh), Sarika Gupta (Panchkula)

Solved Puzzle #38.2: Sunita & Naresh Dhillon (Gurgaon), Sanjeev Varghese (Thane West), Shishir Gupta (Indore), Mudit Singhal (Mumbai)

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