In a Tug of War competition there have been the following results:
Two boys and three girls beat their father,
The mother beat one boy and four girls,
And the father and one boy beat the mother and three girls.
What would be the outcome if the mother and two boys took on the father and three girls?
Assume that all boys pull equally and all girls pull equally.
If you add together the winnings teams from the first two results you get MBBGGG, and if you add together the losing teams you get FBGGG. Removing a boy and three girls from each leaves MB and FG, so we can assume the the mother and a boy would beat the father and a girl - MB beats FG.
Then add the third winning team (FB) to the MB above and you get FMBB, and adding the third losing team (MGGG) to the FG above gives FMGGGG. Removing the father and mother from both sides gives BB and GGGG, so two boys beat four girls, and it follows that a boy would beat two girls - B beats GG.
So MB beats FG and B beats GG. Adding the winning teams gives MBB, and adding the losing teams gives FGGG - the two teams for which we are determining the result.
The mother and two boys will beat the father and three girls.