“We – A, B and C – each have some children.
(i) A has at least one girl and twice as many boys as girls.
(ii) B has at least one girl and three times as many boys as girls.
(iii) C has at least one girl and three more boys than girls.
(iv) When I tell you the number of children we have – a number less than 25 – you will know how many children I have, but not how many children each of the others has. Altogether we have……..”
Who is the speaker and how many children does the speaker have?
(In reply to
Puzzle Answer by K Sengupta)
From (i), it follows that the number of children A has is a multiple of 3. That is: 3,6,9,12,15,18,21,24,.... are the possibilities.
From (ii), it follows that the number of children B has is a multiple of 4. That is:4,8,12,16,20,24,.....
From (iii), it follows that the number of children C has is (1+4)=5 with an increment of 2 for each subsequent possibility. -- that is: 5,7,9,11,13,15,17,19,21, 23.....
Then, the smallest total number of children is 3+4+5=12 and the largest total number of children is 24 in terms of (iv). If the total number of children is even, A will have an odd number of children and, if the total number of children is odd, A will have an even number of children.
The total number of children cannot be 13 because the possibilities for A, B, and C cannot equal that sum.
The total number cannot be 12,14,15,16, or 17 because, then the the total number of children each had would be known, contradicting (iv).
The total cannot be 18,20,21,22,23, or 24 because then no number of children would be known to anybody, again contradicting (iv). So, the total number of children A,B, and C together has must be equal to 19.
When the total is 19, A must have an even number of children and from the possibilities for A,B, and C - this number must not be greater than 19-(4+5)= 10
So, A must have 6 children and, B and C together must have 13 children.
In this situation, (B,C) = (4,9), or (8,5).
Consequently, it is now clear that the speaker is A.
Edited on July 27, 2022, 10:41 pm
Explanation to Puzzle Answer
