Question

A is allowed to select any date of the year other than December 31. B may then select any date later in the same month or the same day of any later month. For example, if A selects June 16, then B may choose any later date in June or the 16th of any month from July to December. Using the same rule with regard to the date that B has selected, A must select a new date, and so on. The winner is the player who arrives at December 31

(a) What date should A select to begin with in order to ensure the fastest possible win?

(b) What if A must start with a date in January? ([27], May 1971).

Full shown work and answer please.

Answer 1

As per the given conditions..the puzzle is solved.....

(a) fastest possible win for A

to select a date as nov 30...then B has only chance to select a date i.e, dec 30...then A can select dec 31st...and A wins...So,if A selects nov 30 then A will win with the  least turns...this the fastest possible win for A to select date as nov 30

(b) If A selects any date from January,,then the possibilities of winning....

if A select january 31st..then B can select dec 31st and B wins..

if A select january 30th..then B can select nov 30..then A has only chance to select date as dec 30 then B can select 31st so B wins...

if A select january 29th..then B can choose jan 30 or jan 31st..or 29th of any month...if B choose jan 30 or 31st then A wins...as per above conditions...if B selects any month of 29th then if A chooses 30th of that same month then A looses..so to win the only possibility for the next step is to select 29th of other month..the same B also do..then who will select the nov 29th first then they will loose....so this possibility has equal chances to win for both of them..

even,the same process is same for remaining dates of january...

so,,finally A has to select other than jan 30th jan 31st to survive for the next turns....it may have chances to win...

The description is clearly written...if you have any doubt ask in the comment section....THANK YOU :-)