The ages of seven children Abner, Belinda, Carl, Deirdre, Ethan, Francine and Gavin are 1, 2, 3, 4, 5, 6 and 7 years in some order. It is known that:

1. Deirdre is precisely three times as old as Belinda.
2. Carl is four years older than Ethan.
3. Francine is older than Abner and Abner is older than Gavin.
4. Combined ages of Abner and Gavin is greater than the age of Francine.

What are the ages of the seven children?

Let the first initial of their name represent the individual's age in years.

1) D = 3B 
∴  B=1 or B=2
   D=3    D=6

2) C = E+4
∴  B=1 or B=2 or B=2
   C=6    C=5    C=7      
   D=3    D=6    D=6
   E=2    E=1    E=3

3) F > A > G
∴  A=5 or A=4 or A=4
   B=1    B=2    B=2
   C=6    C=5    C=7      
   D=3    D=6    D=6
   E=2    E=1    E=3
   F=7    F=7    F=5
   G=4    G=3    G=1

4) A+G > F
∴, with 5+4 > 9 and 4+3=7 and 4+1=5,
   A=5  Angela is 5 years old
   B=1  Belinda is 1 year old
   C=6  Carl is 6 years old       
   D=3  Deirdre is 3 years old
   E=2  Ethan is 2 years old
   F=7  Francine is 7 years old
   G=4  Gavin is 4 years old

Posted by Dej Mar on 2014-11-25 01:20:40