| From the introduction, each Palmer child scored his or her hole-in-one on
a different hole of the 18-hole miniature golf course. By clue 1, Alexis
scored her hole-in-one 6 holes before another child aced the Loop-D-Loop;
while by clue 5, the child who played with the orange ball scored a
hole-in-one 6 holes before Brendan did. Since Alexis didn't use the orange
ball (clue 11) and the child who used the orange ball didn't ace the
Loop-D-Loop (clue 9), four different children are named between the two
clues. In clue 8, then, where the Palmer child who used the blue golf
ball scored a hole-in-one 6 holes before a sibling aced the Parachute,
there must be some commonality with clue 1 or clue 5 or six different
children would be named among the three clues. Since Brendan
didn't use the blue ball (2) and the player who scored a hole-in-one on
the parachute didn't use the orange ball (11), clue 8 does not overlap
with clue 5. Since Alexis didn't score her ace on the Parachute (11),
the player who used the blue golf ball scored a hole-in-one on the
Loop-D-Loop. So, we have all five Palmer children named: Alexis scored
a hole-in-one 6 holes before her sibling who played with the blue ball
aced the Loop-D-Loop and 12 holes before another sibling scored a
hole-in-one on the Parachute, while the player who used the orange ball
scored a hole-in-one 6 holes before Brendan did. By clue 3, either Alexis
or the golfer who used the orange ball aced the 1st hole on the course.
If the child who played the orange ball aced the 1st hole, Brendan would have
scored a hole-in-one on the 7th hole (5). By clue 10, the child who played
with the red golf ball scored a hole-in-one 9 holes before one of the
Palmer children aced the Windmill. If Brendan were the one who used the red
ball, Alexis would have aced the Windmill, which would be the 16th hole.
However, the Loop-D-Loop would then be the 22nd hole (1)--no, since the
course is 18 holes. If Alexis were the one who used the red ball, there
would be no way for the Windmill to fit 9 holes later. If the child who
aced the Parachute had used the red ball, there would again be no way for
the Windmill to fit 9 holes later. So, the child who used the orange ball
didn't ace the 1st hole; Alexis did. The Loop-D-Loop is then the 7th and
the Parachute the 13th hole. Again by clue 10, the child who used the red
ball scored a hole-in-one 9 holes before the child who aced the Windmill.
The child who used the red ball couldn't have aced the Parachute or the
Windmill would be the 22nd hole. Brendan couldn't have used the red ball
because Alexis would then have aced the Windmill. So, Alexis used the red
ball, and the Windmill is the 10th hole. Brendan didn't ace the Windmill
(2), so the child using the orange ball did. Brendan scored a hole-in-one
on the 16th hole (5). By clue 3, the 1st hole is the Ski Jump and the 16th
is Double Trouble. If in clue 7 Chad had aced the 13th hole (the Parachute),
Brendan would have used the yellow ball and Chad then the green--no (4).
Chad scored a hole-in-one at the Windmill, and the golfer who aced the
Parachute did so with a yellow ball (7). Brendan played with a green ball.
Finally, by clue 6, Erica aced the Parachute and David the Loop-D-Loop. In
sum, the Palmer scored holes-in-one on the Summerset Mini-Putt course as
follows:
- Alexis, using the red ball, on 1--the Ski Jump
- David, using the blue ball, on 7--the Loop-D-Loop
- Chad, using the orange ball, on 10--the Windmill
- Erica, using the yellow ball, on 13--the Parachute
- Brendan, using the green ball, on 16--Double Trouble,
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