Problematics | Money transfer
Here’s a simple diversion if you transfer four coins of different sizes from one location to another, following certain rules. In how many moves can you do it?
In the coins we use in India, size is not always directly related to denomination. The best example of this is the ₹5 coin, which is smaller than a ₹1 or ₹2 coin. However, there have been so many coins over the decades that I did not have to think too much before finding four coins that do follow such a relation.

A ₹10 coin is 27mm in diameter, and there are versions of ₹2, ₹1 and 50p coins that measure 25mm, 21.9mm and 19mm respectively. In this set, at least, a larger coin means a higher denomination.
# Puzzle 112.1
Given that any coin of a higher denomination is larger than any coin of a lower denomination, take four of them — ₹10, ₹2 and ₹1 and 50p — and three saucers. Place the four coins on the first saucer, one on top of the other, the largest one at the bottom and the smallest on top. Your task now is to transfer all the coins from the first saucer to the third, using the second saucer as an intermediary. In the end, the four coins need to be on the third saucer in the same order as they were in the first.
There are, of course, rules to follow:
(1) You may transfer only one coin at a time, moving it from any saucer to any other saucer. This comprises one “move”.
(2) At any move, you may transfer a coin to an empty saucer or to a saucer that already has one or more coins on it.
(3) On any saucer at any stage, a coin must be smaller than each of the coins below it.
Can you describe the complete transfer, step by step? Also try to find a general formula giving the number of moves required depending on the number of coins but always using three saucers.
# Puzzle 112.2

MRS ANA BREAKS THE WATER JUG IN THE PANTRY CAR
The above sentence, which consists of 37 letters, is a combined anagram for the names of three superstars who ruled Hollywood in the 1940s and 1950s. The name of the actress has 16 letters while the two actors’ names have 9 and 12 letters respectively, with the cells in the illustration giving the breakups for their names and surnames.
This puzzle might be a little tough (although readers may prove me wrong), so here are a few clues:
(1) In the 1940s, the three superstars acted together in a classic romcom.
(2) Actor #2 won an Oscar Award (Best Actor in a leading role) for his role in that film.
(3) The actress in the anagrams was nominated (Best Actress in a leading role) for her role in the same film, but didn’t win.
(4) The film itself was nominated for Best Picture, but didn’t win.
Can you identify the three superstars and the film?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 111.1

Dear Mr Kabir,
The solution to the Nobel Prize puzzle is shown in the table.
— Shri Ram Aggarwal, Delhi
#Puzzle 111.2
Hi Kabir,
The motorist cannot manage it. If he has to average a given speed, here 80km/h, for the entire distance, let's say 2d (Delhi to Agra and back), he would need to complete it in, let's say, t hours. Now one leg of the journey, i.e. half the distance, is completed in 40km/h, so time taken is t, hence the remaining half of the distance would need some extra time. Hence average speed for the total distance would be less than 80km/h.
— Sabornee Jana, Mumbai
Solved both puzzles: Shri Ram Aggarwal (Delhi), Sabornee Jana (Mumbai), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Sanjay Gupta (Delhi), Kanwarjit Singh (Chief Commissioner of Income-Tax, retired), Professor Anshul Kumar (Delhi), Ajay Ashok (Delhi), Aditya Krishnan (Coimbatore)
Solved #Puzzle 111.1: Anil Khanna (Ghaziabad)
Solved #Puzzle 111.2: Sanjay S (Coimbatore), YK Munjal (Delhi)
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com
