| By clue 1, the six hitting stars averaged from a low of .400 to a high of
.500 at the plate, with no two having the same batting average.
Three Little Leaguers are given in each of clues 4 and 8, so that either
there is some commonality between the clues or all six batting leaders are
named between the two clues. First, we will test all the possible overlaps
between the two clues: 1. Cobb is the shortstop (SS) (and Tommy is then the
third baseman (3B), since no two players had the same batting average (clue
1)); 2. Cobb is Tommy; 3. Bonds is the 3B; 4. the SS plays
for Keystone Bank; 5. Tommy plays for Keystone Bank; and 6. Bonds plays
for Keystone Bank. Possibility 1. contradicts clue 11, which says Tommy
isn't the 3B. If Cobb were Tommy, then between clues 4 and 8, five of the
six league leaders would be named: Tommy Cobb batting X, the SS batting
X+.025, Bonds at X-.015, the 3B averaging X-.025, and the Keystone Bank
slugger hitting X-.050. Either the SS or the sixth player to the five named
would then be the .500 hitter. If the SS were averaging .500, Tommy Cobb
would be at .475, Bonds at .460, the 3B at .450, and the Keystone Bank
player at .425. By clue 1, the sixth player would have averaged .400.
By clue 2, Danny, Paige, and the Reliable Insurance player finished
consecutively highest-to-lowest in the order. Danny would have to be the 3B
and Paige then the Keystone Bank star--no (14). If the sixth player
were batting .500, then the Keystone Bank star would have to be the .400
hitter in clue 1, with the 3B averaging .425, Bonds .435, Tommy Cobb .450,
and the SS .475. By clue 2, then, Danny would have batted .500, Paige would
be the SS, and Tommy Cobb would have led Reliable Insurance--a conflict
with clue 5. Therefore, possibility 2. above, that Cobb is Tommy, fails.
Trying possibility 3., that Bonds is the 3B, between clues 4 and 8, Bonds
would have averaged X, Tommy X+.015, the SS X+.040, Cobb X+.025, and the
Keystone Bank star X-.025. Either the SS or the sixth player to these five
then would have led the league with a .500 average (1). If the SS had averaged
.500, then Bonds would have batted .460, Tommy .475, Cobb .485, and the
Keystone Bank player .435, so that the sixth player would have had the
.400 average (1). However, since Danny isn't Cobb (5) and Paige isn't
the Keystone Bank player (14), there is no way for clue 2 to work. If
the sixth player had averaged .500, then the Keystone Bank player would have
had the lowest average of the six, .400 (1). Bonds would have batted .425,
Tommy .440, Cobb .450, and the SS .465. However, since Cobb isn't Danny
and Cobb isn't on the Reliable Insurance team (5), there is no way for clue
2 to work. Therefore, possibility 3. above, that Bonds plays 3B, fails.
Testing possibility 4., that the SS plays for the Keystone Bank team,
the SS would have averaged X, the 3B X+.025, Cobb X+.050, Tommy X-.025,
and Bonds X-.040. Either Cobb or the sixth player would have hit
the league-leading .500 (1). If Cobb had averaged .500, the SS would have
batted .450, the 3B .475, Tommy .425, and Bonds .410, with the sixth of
the league leaders then batting .400 (1). Since Danny isn't Cobb (5) and
Paige doesn't play for the Keystone Bank nine (14), Danny would be the SS,
Tommy would be Paige, and Bonds would play for Reliable Insurance (2).
However, there is no way for clue 13 to work with this arrangement.
If the sixth player had led the league with a .500 average, then Bonds would
have batted .400 (1) with the SS at .440, Tommy at .415, the 3B at .465,
and Cobb at .490. Since Danny isn't Cobb (5) and Paige doesn't play for the
Keystone Bank team (14), Danny would be the SS, Tommy would be Paige, and
Bonds would play for Reliable Insurance (2). Again, however, there is no way
for clue 13 to work with this arrangement. So, possibility 4., that the SS
is on the Keystone Bank squad, fails. Trying possibility 5., that Tommy is
on the Keystone Bank team, then Tommy would have batted X, the SS X+.025
(4), and the 3B X+.025 (8)--a conflict, since no two averaged the same (1).
Finally, trying possibility 6., that Bonds plays for Keystone Bank, Bonds
would have averaged X, Tommy X+.015, the 3B X+.025, the SS X+.040, and Cobb
X+.050. Either Cobb or the sixth Little Leaguer would have batted .500 (1).
If Cobb had averaged .500, Bonds would have hit .450, Tommy .465, the 3B
.475, and the SS .490, with the sixth man then trailing at .400 (1).
Since Danny isn't Cobb (5), Danny would be the SS, Paige would be the 3B, and
Tommy would play for Reliable Insurance (2). By clue 10, Ruth would be Danny
and Jackie would be Paige--a
conflict with clue 14. If the sixth man had averaged .500 and Bonds then .400,
Tommy would have hit .415, the 3B .425, the SS .440, and Cobb .450. Again, since
Danny isn't Cobb (5), Danny would be the SS, Paige would be the 3B, and
Tommy would play for Reliable Insurance (2). By clue 12, Cobb would be the
left fielder (LF). By clue 13, the 1B would have hit .500, and Bobby would be
Cobb. Then by clue 10, Jackie would be Paige--no (14). So, possibility 6. also fails
and we know that all six players are named between clues 4 and 8. Then
either the SS or Cobb batted .500 (1). If Cobb had batted .500, the 3B
would have hit .475 and the Keystone Bank player .450 (8). Then the low
hitter of the six would be Bonds at .400 (1), with Tommy at .415 and the
SS at .440 (4). By clue 12, the LF would be on the Keystone Bank team;
while by clue 13, Cobb would be the 1B and Bobby the LF. Since Danny isn't
Cobb (5) and Paige doesn't play for the Keystone Bank team (14), by clue 2,
Danny would play SS, Paige would be Tommy, and Bonds would be
on the Reliable Insurance nine. However, there is no way for clue 10 to work
with this arrangement. So, Cobb didn't average .500; the SS did, with Tommy
batting .475 and Bonds .460 (4). In clue 8, the Keystone Bank star would
have batted .400 (1), with the 3B at .425 and Cobb hitting .450. Since
Danny isn't Cobb (5), in clue 2, he plays SS, Paige is Tommy, and Bonds is
on the Reliable Insurance team. By clue 10, Ruth plays 3B, and Jackie is
on the Keystone Bank team. Tommy is the 1B and Bobby Ruth (13). By clue 12,
Andy is Bonds, Cobb plays LF, and Jackie is Ott. By elimination,
Cobb is Mickey and Danny Young. Ott plays right field (RF) and Bonds catcher
(C) (6). Danny Young doesn't play for Qwik Stop (7), Frank's Diner, or
the Lions Club (9) and plays for Valley Lumber. Neither Tommy (3) nor Bobby
(13) is on the Lions Club team, so Mickey is. By clue 11, Tommy plays for
Frank's Diner and Bobby for Qwik Stop. In sum, the six leading batters in
the Summerset Little League this year are
- Danny Young, SS, Valley Lumber, .500
- Tommy Paige, 1B, Frank's Diner, .475
- Andy Bonds, C, Reliable Insurance, .460
- Mickey Cobb, LF, Lions Club, .450
- Bobby Ruth, 3B, Qwik Stop, .425
- Jackie Ott, RF, Keystone Bank, .400
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