WHO M I ?
At the party there were 19 females, 12 males, 14 adults and 17 children. Then I arrived and the number of different man-woman couples possible became equal to the number of boy-girl couples possible.
Who am I - a man, a woman, a boy or a girl?
SOLN :
You are a woman. I ran through all the possible combinations, given 14 adults, 15 adults, 17 children, and 18 children. The only time the combinations were equal, when only one person was added to one of the existing groups, was when the total number of combinations is 45. That's by adding one adult, to make 18, or 15 and 3. The children would be split 9-5
to make 45. I then looked at the numbers: 3, 5, 9 and 15, and realized that there are 20 females and 12 males. The group of 18 (17+1) is the kids, so you're a girl.
The answer is a female child.
By choosing one person type (I used male child), altering that number will have a single possible effect on all other numbers. This makes trial and error easy. I started with 7 male children, then reduced that number until there were:
3 male children ,9 male adults ,5 female adults ,14 female children This makes 42 children couples and 45 adult couples. One more female child would make 15 female children, making 45 child couples
At the party there were 19 females, 12 males, 14 adults and 17 children. Then I arrived and the number of different man-woman couples possible became equal to the number of boy-girl couples possible.
Who am I - a man, a woman, a boy or a girl?
SOLN :
You are a woman. I ran through all the possible combinations, given 14 adults, 15 adults, 17 children, and 18 children. The only time the combinations were equal, when only one person was added to one of the existing groups, was when the total number of combinations is 45. That's by adding one adult, to make 18, or 15 and 3. The children would be split 9-5
to make 45. I then looked at the numbers: 3, 5, 9 and 15, and realized that there are 20 females and 12 males. The group of 18 (17+1) is the kids, so you're a girl.
The answer is a female child.
By choosing one person type (I used male child), altering that number will have a single possible effect on all other numbers. This makes trial and error easy. I started with 7 male children, then reduced that number until there were:
3 male children ,9 male adults ,5 female adults ,14 female children This makes 42 children couples and 45 adult couples. One more female child would make 15 female children, making 45 child couples
Note : that if there were 9 boys and 8 girls at the party, then there would have been 72 (9x8) boy-girl couples possible.
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