Family planning
My mother dreamed of having nineteen children. Her dream didn't come true. But I have three times as many sisters as first cousins, and I have half as many brothers as sisters. How many children did my mother have?
It's all not true.
It's all not true.
Labels: mathschallenge
posted by Chris at
6:21 PM
5 Comments:
answer 1:
10
(2 cousins)
6 sisters
3 brothers
and yourself
answer 2:
(o cousins)
you are an only child
Number of sisters is a multiple of three over first cousins, and a multiple of two over brothers.
So, I have 6, 12, 18, 24, . . . sisters, and 9, 18, 27, .. . siblings altogether. Add one for myself to get the total number of children: 10, 19, 28, . . .
If my mother's dream of 19 children not coming true means that she has LESS than 19 then we are left with an answer of 10 chldren.
What do you mean "it's not all true"? If this is intended to sow seeds of doubt, it has succeeded!
You both got it. The truth is that my real mother didn't want 19 kids. She got 4 boys though.
My pre-prepared answer:
Let s number of sisters. s is a multiple of 2 and 3, so it must
be a multiple of 6, let s = 6m where m is an integer.
Altogether there are 1 + s + s/2 = 1 + 1.5*6m = 1+9m ≤ 19. So,
9m < 18 => m < 2. As m > 1 (else I'd be an only child), m = 2
is the only possibilty, so there are 10 siblings (me, 3 brothers, 6 sisters (and 2 first cousins)).
I came up with 10, but couldn't understand the cousins reference.
The cousins reference was just to say that the number of sisters was a multiple of 3.
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