A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?
Ever since this riddle “a girl has as many brothers as sisters” appeared online, many have tried to answer it and only few have been able to get its answer right.
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The correct answer to a girl has as many brothers as sisters riddle is:
4 daughters (sisters) and 3 sons (brothers).
Logical explanation :
A young lady has the same number of siblings as sisters:
If one of the little girls check her siblings, she would tally – 3 sisters (3 remaining daughters in the family) and her 3 siblings (3 sons in the family).
In this way, it offers the expression genuine that the young lady has the same number of siblings as sisters.
Every brother has just half the same number of brothers as sisters.
This implies, when one of the sons tally his siblings, it would be 2 brothers(staying 2 sons of the family) and 4 sisters (All 4 daughters the family). 2 is half of 4. It consents to the condition that every sibling has just half the same number of brothers as sisters.
Mathematical explanation :
From the reference frame of one of the sisters, there are n sisters and n brothers.
However, from the reference frame of a parent, we see the sister did not include herself in the counting.
This means that there are n boys and n+1 girls.
From the reference frame of one of the brothers, there are n-1 brothers (since he wouldn’t count himself), and n+1 sisters. Also, each brother sees k brothers and 2k sisters.
As a result, we can combine these deductions to create the equation 2(n-1) = n+1. Solving, we find n=3.