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Problematics | Poirot probes Tolstoy
Three Agatha Christie characters are reading different works by the Russian author, but which one is reading what?
Leo Tolstoy’s 197th birth anniversary went during the week between last week’s Problematics and this episode. Also, Agatha Christie’s 135th happens to fall on the day this is being published. The two events give us an excuse (not that we need one) to have a fun puzzle based on Tolstoy’s writings and Christie’s characters.
#Puzzle 160.1
Hercule Poirot, accompanied by Captain Hastings, are at a library where they meet Miss Marple at a shelf displaying Russian literature. With no crime case to solve, the two detectives and the retired soldier agree to puzzle each other instead. Each one of them will take a book by Tolstoy, but with several strings attached:
(1) Poirot will not read War and Peace unless Hastings reads Anna Karenina
(2) Poirot will not read Resurrection unless Miss Marple reads War and Peace
(3) Poirot will not read Anna Karenina unless Hastings reads Resurrection
(4) Miss Marple will not read War and Peace unless Poirot reads Anna Karenina
(5) Hastings will not read Resurrection unless Miss Marple reads Anna Karenina
Who will read what?
#Puzzle 159.1
On January 25 and May 5 this year, the dates 25/1/25 and 5/5/25 represented two simple multiplications: (5 x 5 = 25) and (25 x 1 = 25). Written in the format date/month/year, four dates in 2028 will have this property: 28/1/28, 14/2/28, 7/4/28 and 4/7/28.
Which year in this century (2001-2100) has the highest number of such dates?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 159.1
Dear Kabir,
There are two possible cases: (1) the person sitting next to two men is a man; and (2) the person sitting next to two men is a woman. The only possible sitting arrangements for these two cases are shown in Figure 1, with women and men denoted by W and M respectively. In this figure, seats are numbered clockwise from 0 to 7, starting with the seat of the person sitting next to two men.
Now the hostess is the only person sitting between a couple. After considering various possibilities for the hostess and the couple sitting around her, it can be seen that no valid solution exists for Case 2 (with a woman sitting between two men). A valid solution, however, is possible for Case 1 as shown in Figure 2. Here, Mr Chaturvedi is sitting between Mr Bhardwaj and Mr Dasgupta.
— Professor Anshul Kumar, New Delhi
#Puzzle 159.2
Dear Kabir,
Yes, I can answer the question about the cards: there are as many red cards in the left-hand pile as there are black cards in the right-hand pile. This is because after dividing the pack of 52 in two equal piles, there will be 26 cards in each pile. Now there are totally 26 red and 26 black cards in the whole deck. Hence if the number of red cards in the left pile is x, then the number of black cards in that same pile will be (26-x). Hence the remaining number of black cards that will be found in the right pile will be 26-(26-x) = x.
— Dr Nitin Trasi, Sydney
For Puzzle 159.1, there is more than one possible arrangement, but Mr Chaturvedi is always the one sitting between two men. Vinod Mahajan provides an alternative arrangement: (going clockwise) Mrs Ahmed, Mr Bhardwaj, Mr Chaturvedi (he has a man on each side), Mr Dasgupta, Mrs Dasgupta, Mrs Chaturvedi, Mr Ahmed, Mrs Bhardwaj (the hostess, between Mr and Mrs Ahmed).
Solved both puzzles: Professor Anshul Kumar (Delhi), Vinod Mahajan (Delhi), Dr Vivek Jain (Baroda), Sanjay Gupta (Delhi), Shri Ram Aggarwal (Delhi)
Solved #Puzzle 159.2: Dr Nitin Trasi (Sydney), Yadvendra Somra (Sonipat), Anil Khanna (Delhi), Ajay Ashok (Delhi), Kanwarjit Singh (Chief Commissioner of Income-tax, retired), YK Munjal (Delhi)
