Ron Barnette's Zeno's Coffeehouse Challenge #48 Result
Dear Zeno's patrons: Here are the results of our previous challenge. I have listed the original problem, with the winning results listed below. Thanks to all you Zeno's patrons who took up the challenge!
In the latest standings for long distance
swimming at The Zeno's Coffeehouse Swim Clubs (seems that our man Charles established
these clubs last summer, which are indoor club pools, for local youth groups during the
winter months), Marcie and four other girls top the list for most distance in one swimming
session at their respective club pools, one of which is Aspen Terrace. Each club leader's
best effort is a different number of laps. Given the clues that follow, you are to deduce
the full name (one surname is Waters) and home club pool of each swimmer and the number of
laps she has totaled to lead the charts.
Results:
There were only seven winning solutions submitted! The winners were Rachel Agent, Mark Young, Hunter Lane, Jordan Kynes, Troy Williamson, Tim Whealan, and Helen Wishart. CONGRATULATIONS!!!
I include below the solutions from Rachel Agent and Mark Young, who developed excellent reasoning:
Rachel Agent....comments: I am not really good at
explaining myself, nor the way my mind works. However I will try -
From the first clue, a person can gather that the most laps is 200 and the least is 80.
therefor three numbers reamain.
The second clue tells us this: since the River's girls best effort is twice that of
the girl from maple creek then we know that the girl from maple creek can not be the girl
whose best effort was 200 -BUT EVEN MORE SO- we know the girl from maple creek can not be
more that 100, since 101x2=202 (which is more than 200 the most of the girls laps)
Also since the River's girl does double the amount of laps as the Maple Creek girl
than we know that she must at least do 160 laps - since 80 laps is the least of the girls'
laps.
The third clue reveals basically the same thing- since Katie has swam 40 laps more than
the Brooks girl than Katie must have swam at least 120 laps(CONSIDERING THE BROOKS GIRL
MUST SWIM AT LEAST 80 LAPS) however Katie also swam 80 laps more than the Oak Ridge girl
therefore bringing the least amount of laps Katie could have done to 160.
The fouth clue AGAIN, the same thought process- Jenny also can not be under 160 whereas
the Poole girl cannot be over 100.
The real clue comes in the last one- Carrie, who isnt the lake girl, has swam 40 more laps
than the swimmer from beach shore. Meaning beach shore can not be 200, but also
meaning that Carrie can not be 80, nor 100. She could however be 200,160, or 120.
YET didnt we just say that NOT ONLY MUST Katie be 160 or 200, but also JENNY MUST
BE TOO!! AH HA!!! CARRIE MUST THAN BE 120 and since Carrie is 120 than Beach shore must
then 80. RIGHT!! ARE YOU STILL WITH ME. if not here is
a diagram.
Rivers
-> Katie (must be 160 or above)
| Jenny
|------>Carrie
must be 120 or
|
|
above and since Katie
| 200
|
and Jenny take up the
|_________160
|
160 and 200 slot
__________120_____________|
Carrie must be 120
| 100
| 80
|
|---> Maple Creek and Poole girl must be 100 or below
now that you have that figured out you have basically broke the code.
Go back up to clue #2. Since the rivers girls best effort is twice that of
the girl from Maple Creek you know that Rivers must be 200 and Maple Creek 100 since 80
and 160 are used, and since it tells you that the girl from Maple Creek( 100 or less laps)
is not Vicki it has to be Marcie considering Jenny and Katie must have 160 or 200 laps and
there is noone left BUT MARCIE.
If you continue reading each clue and deducting the obvious the answer should come to you
pretty shortly...It helps if you use an L- grid
So it is my conclusion that the answer is, when based on the even numbers of 80, 100, 120,
160, and 200, as follows:
80 - Vicki Poole from Beech Shore
100- Marci Lake from Maple Creek
120- Carrie Waters from Oak Ridge
160- Jenny Brooks from Aspen
and
200- Katie Rivers from Pine Valley
Mark Young.....comments: The values we are working
with are:
First names: Marcie, Vicki, Katie, Jenny, and Carrie.
Last names: Waters, Rivers, Brooks, Poole, and Lake.
Clubs: Aspen Terrace, Maple Creek, Oak Ridge, Pine Valley,
and Beech Shore.
Each clue (2 thru 5) says something about two or three
swimmers, and so I have introduced letters to indicate the
different swimmers mentioned in each clue. The number/letter combinations in
(parentheses) indicate
positive information about a swimmer, while the ones in [brackets] indicate negative
information.
2. The Rivers (2a) girl's best effort is twice as many laps as that of the swimmer from
Maple Creek (2b), who isn't Vicki [2b].
3. Katie (3a) has swum 40 more laps than the Brooks (3b) girl and 80 more than the Oak
Ridge (3c) pool leader.
4. Jenny (4a), who isn't the Pine Valley [4a] member, has twice as many laps as the Poole
(4b) girl.
5. Carrie (5a), who isn't the Lake [5a] girl, has swum 40 more laps than the swimmer from
Beech Shore (5b).
Clue 1 tells us that there is a swimmer with 200 laps, another
with 80 laps, and each of the three others has between 80 and
200. We also know that each swimmer has a different number of
laps.
The numbers of laps are further restricted by the clues. If
swimmer X has twice as many laps as swimmer Y, then swimmer X
must have at least 160 laps (since swimmer Y has at least 80),
and swimmer Y must have at most 100 laps (since swimmer X has
at most 200).
So here are the clues again -- positive information only --
broken down by swimmer, and showing the range of laps allowed:
2a. (160 to 200) laps for --- Rivers of ---.
2b. (80 to 100) laps for --- --- of Maple Creek.
3a. (160 to 200) laps for Katie --- of ---.
3b. (120 to 160) laps for --- Brooks of ---.
3c. (80 to 120) laps for --- --- of Oak Ridge.
4a. (160 to 200) laps for Jenny --- of ---.
4b. (80 to 100) laps for --- Poole of ---.
5a. (120 to 200) laps for Carrie --- of ---.
5b. (80 to 160) laps for --- --- of Beech Shore.
We'll start by showing that the Oak Ridge girl (swimmer 3c, that
is, in the list of clues shown above) must have 120 laps. We
will show that by showing no other value works for her.
Suppose the girl from Oak Ridge (3c) has 80 laps.
Then the Brooks girl (3b) has 120, and Katie (3a)
has 160. We summarize that with a little chart:
200 laps for --- --- of ---
160 laps for Katie (3a) --- of ---
120 laps for --- Brooks (3b) of ---
80 laps for --- --- of Oak Ridge (3c)
Now the girl from Maple Creek (2b) can't
have 80 laps (since the girl from Oak Ridge has 80
laps). However many laps she does have, there
must be someone with twice as many, and since the
only other person in the mix has 200 laps, 2b must
have half that -- that is, 100 laps.
200 laps for --- Rivers (2a) of ---
160 laps for Katie (3a) --- of ---
120 laps for --- Brooks (3b) of ---
100 laps for --- --- of Maple Creek (2b)
80 laps for --- --- of Oak Ridge (3c)
Next, since 80 and 100 are taken by other clubs,
the girl from Beech Shore (5b) must have either
120 or 160 laps. But Carrie (5a) can't have 160
(since Katie has 160), so Beech Shore must be 160
and Carrie 200. That gives us
200 laps for Carrie (5a) Rivers (2a) of ---
160 laps for Katie (3a) --- of Beech Shore (5b)
120 laps for --- Brooks (3b) of ---
100 laps for --- --- of Maple Creek (2b)
80 laps for --- --- of Oak Ridge (3c)
But now we can't fit in (4a) and (4b). Jenny can't
be either 200 or 160, but she can't be less than
160, either.
Conclusion: the Oak Ridge girl has more than 80
laps.
Now suppose Oak Ridge has 81 laps. By clues 1 and 3
there would be swimmers with 80, 81, 121, 161 and
200 laps. But no one has exactly twice as many as
anyone else, which contradicts clues 2 and 4.
Similarly, the Oak Ridge girl can't have 82 to 99
laps, or 101 to 119. None of those values allow
one girl to have twice the laps of another (given
clues 1 and 3, that is).
So what if Oak Ridge had 100 laps? Then we would
have swimmers with 80, 100, 140, 180 and 200 laps.
The only double would be 100 to 200 laps, and so
(2b) would have to have 100 laps -- but (2b) is
from Maple Creek, not Oak Ridge. So 100 laps doesn't work,
either.
Having ruled out every value from 80 to 119 for the
girl from Oak Ridge, only 120 is left.
200 laps for Katie (3a) --- of ---
160 laps for --- Brooks (3b) of ---
120 laps for --- --- of Oak Ridge (3c)
80 laps for --- --- of ---
Since Jenny (4a) can't have 200 laps, and we don't
have room to add two more numbers, she must have
160 laps.
200 laps for Katie (3a) --- of ---
160 laps for Jenny (4a) Brooks (3b) of ---
120 laps for --- --- of Oak Ridge (3c)
80 laps for --- Poole (4b) of ---
Carrie (5a) must have 120 laps. (Any other number leads to a
name conflict or introduces a sixth number into our chart.)
200 laps for Katie (3a) --- of ---
160 laps for Jenny (4a) Brooks (3b) of ---
120 laps for Carrie (5a) --- of Oak Ridge (3c)
80 laps for --- Poole (4b) of Beech Shore (5b)
Now the girl from Maple Creek can't have 80 laps, and
so must have 100.
200 laps for Katie (3a) Rivers (2a) of ---
160 laps for Jenny (4a) Brooks (3b) of ---
120 laps for Carrie (5a) --- of Oak Ridge (3c)
100 laps for --- --- of Maple Creek (2b)
80 laps for --- Poole (4b) of Beech Shore (5b)
We now have only two first names, two last names and two
clubs to assign to the swimmers. We now use the negative information. Since 2b
isn't Vicki, she must be
Marcie. Since 4a is not from Pine Valley, she must be from
Aspen Terrace. Since 5a is not the Lake girl, she must be
the Waters girl.
The remaining values are filled in by elimination.
200 laps for Katie (3a) Rivers (2a) of Pine Valley [e]
160 laps for Jenny (4a) Brooks (3b) of Aspen Terrace [4a]
120 laps for Carrie (5a) Waters [5a] of Oak Ridge (3c)
100 laps for Marcie [2b] Lake [e] of Maple Creek (2b)
80 laps for Vicki [e] Poole (4b) of Beech Shore (5b)