a couple of months ago, Faiq reminded me of a puzzle in endgame in times of india -
find a number n such that if the last digit is moved to first digit, the value is doubled.
eg if n=1234, you move 4 to the front and n becomes 4123 but 4123 is not equal to 1234*2
i had posted one solution to the paper about 5/6 years back using rudimentary approach.
but being the super-geek-nerd phd student, i derived the root family of such numbers (8 such
numbers only) along with a proof that a concatenation of any such number n (n n n.....)
is also a member of the family. so there are infinite such numbers - proof is here :)
the sad thing was, when i contacted the global math repository people, turns out somebody
already proved this 20 years back - damn you, mathematicians :'(
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