Question

Some friends bought some chocolates and hide them in a box and went to sleep. One of
the friends wakeup and ate one chocolate before taking half the number of chocolates.
Now the second friend wake up, did the same and went to sleep. This process continued
until the last person did the same and went to sleep. When they woke up in the morning
only one chocolate was left. If it is known that there are less than hundred chocolates,
then how many friends are there? (to the maximum)

Answer 1

Answer:

We write the number of chocolates,x, starting from the end (when we know that 1 chocolate has remained).

Before remaining one chocolate, there were 2*1 =2 (since the penultimate person takes half).

Before the penultimate person to take 1, there are left 2+1=3

Now, 3 is the half of what is left after the person before the penultimate ate 1 => 3*2 +1 =7 before that

And so forth.

7*2+1 =15

15*2+1=31

31*2+1=63

63*2+1=127 false, since 127 >100

Thus we stop at 63 chocolates and count the persons for obtaining 5 (without the person who finds the last chocolate).

If we also count that person, we obtain 6 friends at maximum.