Quick brain teaser
Jane has twice as many brothers as she has sisters. Her brother, Jim, has one more sister than brothers. How many boys and girls are in the family?
1 blog point to all correct answers within the next couple of days.
Tuesday, March 20, 2007
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Jane's got one sister (X) and two brothers (Jim and Y). Jim has one brother (Y) and two sisters (Jane and X). Four kids, two of each sex: Jane, X, Jim, Y.
Presuming a "traditional" family I suppose you could also include their parents and say there are 3 girls and 3 boys. :)
Solving algebraically, because I love to:
Let g be the # of girls
Let b be the # of boys
From Jane's perspective we get:
2(g - 1) = b (# of girls, excluding her is twice the # of boys)
From Jim's perspective we get:
g = (b - 1) + 1 (one more girl than boy, excluding him)
which simplifies to:
g = b
Subbing the 2nd equation into the 1st:
2(g - 1) = g
2g - 2 = g
g = 2
Therefore b = 2
So there are 2 boys and 2 girls. Optionally add Mom and Dad which would be 3 boys and 3 girls, although that's hardly PC!
bros sis
jane 2x x
jim y y+1
boys = 2x = y+1
girls = y+1 = x + 1
therfore:
x=1
y=1
boys = 2
girls = 2
2 boys, 2 girls.
1) There has to be an even number of boys
2) The number of siblings of the same sex is one less than the total number of that sex
Brute force starting with 1 sister means 2 boys. That 2 boys - Jim = 1 brother for Jim. 1 + 1 = 2, so there are 2 boys, 2 girls.
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