Question 845606
{{{(5/6)*(4/5)*(3/4)*(2/3)*(1/2)*x=3}}}
{{{(5*4*3*2*1/(6*5*4*3*2))*x=3}}}
There is 5, 4, 3, and 2 in numerator and denominator.
They "cancel out" and you get
{{{(1/6)*x=3}}} so {{{x=3*6}}} and {{{highlight(x=18)}}} .
The interesting part is that the king took {{{1/6}}} of {{{18}}} mangoes,
which is {{{(1/6)*18=3}}} mangoes,
and each person after the king took {{{3}}} mangoes too.
of the {{{18-3=15}}} mangoes left, the queen took
{{{(1/5)*15=3}}} mangoes, leaving
{{{15-3=12}}} .
Then from those {{{12}}} the first prince took {{{1/4}}},
which was {{{(1/4)*12=3}}} mangoes, and so on.
Each member of the family calculated his or her share very fairly.
Each one figured that the remaining mangoes were to be divided among the {{{n}}} family members that had not yet received a portion, and took the {{{1/n}}} fair share, so they would all end up with the same amount.