
Grace is 23, Helen is 25,
Mary is 22.
Let us describe each statement according to the following key...
Grace:
G1  I am twentytwo.
G2  I am two years younger than Helen.
G3  I am a year older than Mary.
Helen:
H1  I am not the youngest.
H2  Mary and I are three years apart.
H3  Mary is twentyfive.
Mary:
M1  I am younger than Grace.
M2  Grace is twentythree.
M3  Helen is three years older than Grace.
Removing one statement from each gives 27 different combinations as
follows
1. G1, G2  H1, H2  M1, M2
2. G1, G2  H1, H2  M1, M3
3. G1, G2  H1, H2  M2, M3
4. G1, G2  H1, H3  M1, M2
5. G1, G2  H1, H3  M1, M3
6. G1, G2  H1, H3  M2, M3
7. G1, G2  H2, H3  M1, M2
8. G1, G2  H2, H3  M1, M3
9. G1, G2  H2, H3  M2, M3
10. G1, G3  H1, H2  M1, M2
11. G1, G3  H1, H2  M1, M3
12. G1, G3  H1, H2  M2, M3
13. G1, G3  H1, H3  M1, M2
14. G1, G3  H1, H3  M1, M3
15. G1, G3  H1, H3  M2, M3
16. G1, G3  H2, H3  M1, M2
17. G1, G3  H2, H3  M1, M3
18. G1, G3  H2, H3  M2, M3
19. G2, G3  H1, H2  M1, M2
20. G2, G3  H1, H2  M1, M3
21. G2, G3  H1, H2  M2, M3
22. G2, G3  H1, H3  M1, M2
23. G2, G3  H1, H3  M1, M3
24. G2, G3  H1, H3  M2, M3
25. G2, G3  H2, H3  M1, M2
26. G2, G3  H2, H3  M1, M3
27. G2, G3  H2, H3  M2, M3
The following linked statements are incompatible,
1. G1 ("I am twenty two") and
M2 ("Grace is twenty three")
thus options 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18 are invalid.
2. G2 ("I am two years younger than Helen") and
M3 ("Helen is three years older than Grace")
thus options 2, 3, 5, 6, 8, 9, 20, 21, 23, 24, 26, 27 are invalid.
3. G1 ("I am twentytwo"),
G3 ("I am a year older than Mary") and
H3 ("Mary is twentyfive")
thus options 13, 14, 15, 16, 17, 18 are invalid
4. H3 ("Mary is twentyfive"),
M1 ("I am younger than Grace") and
M2 ("Grace is twentythree")
thus options 4, 7, 13, 16, 22, 25 are invalid
5. G3 ("I am a year older than Mary"),
H2 ("Mary and I are three years apart") and
M3 ("Helen is three years older than Grace")
thus options 11, 12, 17, 18, 20, 21, 26, 27 are invalid
The only remaining valid option is number 19, the following statements
are therefore true.
Grace
"I am 2 years younger than Helen" 
"I am a year older than Mary"
Helen 
"I am not the youngest" 
"Mary and I are three years apart"
Mary 
"I am younger than Grace" 
"Grace is 23"
The rest is simple mathematics starting from Mary's declaration about
Grace's age and Grace's declarations about the age gaps between her
and her friends. 
