Question

Alok went to a casino to play a card game. He
played 10 rounds of that game. In each round, he
doubled his amount and then gave x/- to his friend.
After 10 rounds, he had 1023. Find the sum of the
digits of the least possible value of x. (All the
amounts involved in rupees) are integers)​

Answer 1

Amount with Alok :

Let it be ' z '

1 st Round :

2z - x

2 nd Round :

2 ( 2z - x ) x

= 4z - 3x

3 rd Round :

2 ( 4z - 3x ) x

= 8z - 7x

Therefore , at 10 th Round :

1024 z - 1023 x = 1023

= 1024 z = 1023 ( x + 1 )

= z / ( x + 1 ) = 1023 / 1024

x + 1 = divisible by 1024 &

least value = 1023

= > 1 + 2 + 3 = 6 .

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