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Problematics | Lettered states
A game similar to antakshiri, but with Indian states rather than songs. What is the optimal strategy?
Among the ads that have been appearing during the live streaming of India’s cricket series in Sri Lanka, one plays on an Indian game called antakshiri. You know the rules: a player starts a song, and after he or she breaks off, the next player begins a song with the last letter of the previous song. And so it goes on.
It need not be restricted to songs alone. Children play versions of the game with names of cities, animals, Marvel characters, and what not. It need not be restricted to India either. In America, they have a version called knockout open-end geography, which is played with the names of US states. The rules are more flexible than in antakshiri: a player has the option of naming a state that either begins with the last letter of the previous state or ends in the first letter of the previous state. For example, if the previous state named is Arkansas, the next player can either start with S (South Carolina, for example) or end in A (Nevada among many options).
No state can be named twice. Any player who cannot name a state or UT drops out. The next player then starts a new round with any state. The game is won by the last player standing.
Now let’s customise this with Indian states and Union Territories.
#Puzzle 209.1
India has 28 states and 8 UTs, giving players a significantly narrower field than the 50 US states. Use the standard spellings of the states and UTs as listed on a government website. States and UTs with multiple words in their name count as one unit; for example, in Andaman and Nicobar Islands, take A as the first letter and S as the last letter.
The rules are the same as the American game described above. The first player may name any state or UT. You start with any Indian state, say Manipur, and the next player has the option of either beginning with R (Rajasthan) or ending in M (say Assam). If it’s Rajasthan, the third player can say Nagaland or Bihar; if it’s Assam, the third player can go with Meghalaya (which simultaneously satisfies both the first-letter and last-letter options with Assam).
Martin Gardner wrote about a puzzle associated with the American version, posed by the mathematician and puzzler David Silverman. If three players are playing the game, what is the best strategic opening move for the first player?
There is more than one answer, of which Gardner describes Tennessee as the quickest. No US state starts with E, so the second player must find a state that ends in T. The second player can then name either Connecticut or Vermont. Gardner says this eliminates the third player, because no state ends in C or V. I am not sure if Gardner missed something or if I misunderstood the rules, but to me Texas appears to be an option for the third player. But taking the third player as eliminated, the first player starts a new round. Naming Maine eliminates the second player, because no US state ends in M or starts with E.
Take three Indian players playing with Indian states and UTs. I don’t know the answer to this one, and I don’t even know if the first player can choose a state or UT that ends the game as fast as Tennessee, or if the strategy requires multiple rounds. I would like to see how readers chalk it out, step by step.
Assuming all three players play optimally, what opening move should the first player make to guarantee victory? If you find that more than one opening move does so, which ones gives the quickest victory?
#Puzzle 209.2
A deck of 52 cards is shuffled, and one card is removed at random. The rest of the pack is shuffled again, and another card is removed at random.
What is the probability that both removed cards are the same colour?
MAILBOX: LAST WEEK'S SOLVERS
#Puzzle 208.1
Hi Kabir,
I am at present in USA and hence missed a few episodes of Problematics. My solution to #Puzzle 208.1 after combining the three statements of each girl is that Ananya ate the missing slice of cake. The false statements of five girls are as follows:
Anjana: Anubha ate the missing slice
Anubha: Ankita ate the slice
Ananya: I didn't eat the missing slice
Anjali: Anubha ate the slice
Ankita: I never drink coffee
— Anil Khanna, Fremont
#Puzzle 208.2
Hi,
Because the two cans are the same shape and made of the same material, doubling the height doubles every linear dimension. The volume of the larger can is therefore higher than the volume of the smaller can by a factor of 2³ = 8. The material making up the empty can (surface area) is higher by a factor of 2² = 4.
Let the 6cm can weigh x kg when empty and let the coffee in it be y kg. Then:
x + y = 0.275
For the 12cm can: 4x + 8y = 2.1
Dividing the second equation by 4 and subtracting the second equation,
(4x + 8y)/4 – (x + y) = 0.525 – 0.275
=> y = 0.250
So, the 6cm can contains 250 g of coffee. The 12cm can has 8 times as much, i.e. 2 kg.
— Ajay Ashok, New Delhi
Solved both puzzles: Ajay Ashok (Delhi), Dr Sunita Gupta (Delhi), Vinod Mahajan (Delhi), Professor Anshul Kumar (Delhi), Shri Ram Aggarwal (Delhi)
Solved #Puzzle 208.1: Anil Khanna (Fremont), Dr Vivek Jain (Baroda), Yadvendra Somra (Sonipat), Sabornee Jana (Mumbai)
Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com
