# Logic Puzzle: Antique Bargains at the Hartlan Flea Market

#### Swammerdami

##### Squadron Leader
Staff member
Any interest in logic puzzles? Here's one I like, though it's harder than most.

Antique Bargains

The Hartlan County Flea Market mostly just sells junk but last weekend there was an auction of antiquities. Mr. Ainsworth and six of his friends each went home with what he or she thought was a great bargain. One of the seven antiques was a steel knife dated to Egypt's Old Kingdom.

The friends included three women (Mary, Nancy and Olivia) and four men (one named John). They paid seven different prices for their treasures: $25,$30, $40,$45, $50,$60, $80. From the four clues, determine the full name of each of the seven people, his or her purchase, and the price paid. • Clue 1: The toy wheeled wagon from the Mayan civilization cost$20 more than Mr. Elwell's purchase.
• Clue 2: Miss Brown spent $20 more than Hank. Nancy spent$20 more than Miss Dolliver. Mary spent more than Olivia.
• Clue 3: The four most expensive purchases were, in no particular order, Alexander the Great's wrist watch, the coin with a date-stamp of 42 BC (which cost $15 more than Larry's purchase), Mr. Fairbanks's purchase (which cost$15 more than the photograph of Cyrus the Great), and Nancy's purchase.
• Clue 4: Mr. Clifton's purchase (a pistol from the Battle of Hastings) and the plastic Aztec doll were each gift-wrapped. Neither was purchased by Kenneth or Miss Gifford.

#### Swammerdami

##### Squadron Leader
Staff member
Little interest apparently, but I will bump this once (demonstrating my masochism? ).

Antique Bargains

The Hartlan County Flea Market mostly just sells junk but last weekend there was an auction of antiquities. Mr. Ainsworth and six of his friends each went home with what he or she thought was a great bargain. One of the seven antiques was a steel knife dated to Egypt's Old Kingdom.

The friends included three women (Mary, Nancy and Olivia) and four men (one named John). They paid seven different prices for their treasures: $25,$30, $40,$45, $50,$60, $80. From the four clues, determine the full name of each of the seven people, his or her purchase, and the price paid. • Clue 1: The toy wheeled wagon from the Mayan civilization cost$20 more than Mr. Elwell's purchase.
• Clue 2: Miss Brown spent $20 more than Hank. Nancy spent$20 more than Miss Dolliver. Mary spent more than Olivia.
• Clue 3: The four most expensive purchases were, in no particular order, Alexander the Great's wrist watch, the coin with a date-stamp of 42 BC (which cost $15 more than Larry's purchase), Mr. Fairbanks's purchase (which cost$15 more than the photograph of Cyrus the Great), and Nancy's purchase.
• Clue 4: Mr. Clifton's purchase (a pistol from the Battle of Hastings) and the plastic Aztec doll were each gift-wrapped. Neither was purchased by Kenneth or Miss Gifford.
Speaking of sado-masochism, my policy is to strip away any clue that is redundant — that can eventually be deduced. Since this leads to a shorter set of clues it may make the puzzle appear easier, but of course the opposite is true! I'll add one more small Clue, that will make the puzzle easier:

• Clue 5: The steel knife from Egypt was not the most expensive purchase.

Let me show how I solve puzzles of this type. (The cross-hatch grids sometimes presented are generally NOT the best approach.) First I get all the characters in view:
Forenames are H/J/K/L/M/N/O
Surnames are A/B/C/D/E/F/G
Items are knife/mayan/doll/watch/coin/photo/gun
Prices are $25/30/40/45/50/60/80 (Notice that I replaced "pistol" with "gun" just so I an use "p" as an unambigious abbreviation should that prove convenient. Similarly, I let "m" define the Mayan wagon instead of the ambiguous "w.")​ Then I convert each Clue to a List of different people/purchase/price combinations. "Mr." and "Miss" imply possible forenames. Clue 1 --mayans+20 H/J/K/LElwell-s Clue 2 M/OBrown-t+20 Hank--t Nancy--u+20 M/ODolliver-u Clue 3 --watch80/50 --coin60/45 = Larry+15 H/J/K/LFairbanks-60/45 = photo+15 Nancy-80/50 ---25/30/40 ---25/30/40 ---25/30/40 (In preparing this table, I took advantage that neither 80-15 =$65 nor 50-15=$35 is one of the prices paid.) Clue 4 H/J/LCliftongun- --doll- Kenneth--- M/N/OGifford-- Some of the facts in the Clues won't lend themselves to easy incorporation into these tables. Make a record of them. In this case there was only one: • Mary spent more than Olivia. (From Clue 2) ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Now the fun begins! Merge information from the separate tables. (Right away we see from Clues 2 and 4 that Nancy's surname must be Gifford. You can also deduce Nancy's purchase by elimination.) But I won't pursue this further, in case someone else wants to give it a whack! Don't forget to take advantage of the Hint: "The steel knife from Egypt was not the most expensive purchase." #### Angra Mainyu ##### Veteran Member Any interest in logic puzzles? Here's one I like, though it's harder than most. Antique Bargains The Hartlan County Flea Market mostly just sells junk but last weekend there was an auction of antiquities. Mr. Ainsworth and six of his friends each went home with what he or she thought was a great bargain. One of the seven antiques was a steel knife dated to Egypt's Old Kingdom. The friends included three women (Mary, Nancy and Olivia) and four men (one named John). They paid seven different prices for their treasures:$25, $30,$40, $45,$50, $60,$80.

From the four clues, determine the full name of each of the seven people, his or her purchase, and the price paid.

• Clue 1: The toy wheeled wagon from the Mayan civilization cost $20 more than Mr. Elwell's purchase. • Clue 2: Miss Brown spent$20 more than Hank. Nancy spent $20 more than Miss Dolliver. Mary spent more than Olivia. • Clue 3: The four most expensive purchases were, in no particular order, Alexander the Great's wrist watch, the coin with a date-stamp of 42 BC (which cost$15 more than Larry's purchase), Mr. Fairbanks's purchase (which cost $15 more than the photograph of Cyrus the Great), and Nancy's purchase. • Clue 4: Mr. Clifton's purchase (a pistol from the Battle of Hastings) and the plastic Aztec doll were each gift-wrapped. Neither was purchased by Kenneth or Miss Gifford. Kenneth Ainsworth got Alexander the Great's wrist watch for$80.
Mary Brown got the coin with a date-stamp of 42 BC for $60. Nancy Gifford got the steel knife dated to Egypt's Old Kingdom for$50.
Larry Fairbanks got the toy wheeled wagon from the Mayan civilization for $45. Hank Clifton got a pistol from the Battle of Hastings for$40.
Olivia Dolliver got the photograph of Cyrus the Great for $30. John Elwell got the plastic Aztec doll for$25.

#### Swammerdami

##### Squadron Leader
Staff member
Bravo, Angra Mainyu !

I'm afraid to ask whether you found this to be a fun challenge ... or just a tedious annoyance.

#### Angra Mainyu

##### Veteran Member
Bravo, Angra Mainyu !

I'm afraid to ask whether you found this to be a fun challenge ... or just a tedious annoyance.

It was fun, but it was late at night and I expected it to be faster, so in the end it got somewhat longer than I was planning, which did annoy me a bit - but I wasn't going to leave it for later, or read the post with hints no way.

It's my fault for not turning it into a problem with some variables and functions and instead resolving it with the names and all.

#### Jayjay

##### Contributor
It was a fun challenge... but I messed up somewhere and got the wrong result, and I didn't want to retrace my steps. The fifth extra clue didn't seem necessary though.

#### Angra Mainyu

##### Veteran Member
The fifth extra clue didn't seem necessary though.

It wasn't (which I see Swammerdami also said), but now that I think about, it would have been easier (so, less fun ) if I had read it because I had to rule out that possibility. I don't actually remember whether that part took long or not though. At some point I was thinking { Nancy Gifford's purchase, Alexander the Great's wrist watch}={ purchase that cost $50, purchase that cost$80}, and I think the extra clue would have helped me figure out faster that the watch cost $80. That depends on how one approaches it, though. Last edited: #### Swammerdami ##### Squadron Leader Staff member Puzzles that require "trial-and-error" to solve may be undesirable. (Or not? The harder the better?) But even the term "trial-and-error" is hard to define. Perhaps an adequate working definition would be: "Eliminating a possibility is said to require trial-and-error when the elimination cannot be proven with a single clause of moderate length." With this definition, Antique Bargains at the Hartlan Flea Market does not require trial-and-error, but it is still rather difficult. Especially without the Hint ("Fifth Clue"). If there's interest I'll post a step-by-step solution using neither trial-and-error nor the Hint. Bravo, Angra Mainyu ! I'm afraid to ask whether you found this to be a fun challenge ... or just a tedious annoyance. It was fun, but it was late at night and I expected it to be faster, so in the end it got somewhat longer than I was planning, which did annoy me a bit - but I wasn't going to leave it for later, or read the post with hints no way. It's my fault for not turning it into a problem with some variables and functions and instead resolving it with the names and all. I also have written software to solve puzzles of this sort; I use it to verify the solution and its uniqueness, and to eliminate unnecessary clues. For a while many years ago I composed logic puzzles for Penny Press Logic and Dell Logic. (* - Although their logic puzzle editing styles are very different, these two magazines have the same mailing address and same corporate overlord. — Another example of the American business trend toward consolidation.) If there's sufficient interest I may compose another puzzle to post here. Make it harder? Easier? Based on Liars and Truthers? #### Angra Mainyu ##### Veteran Member Puzzles that require "trial-and-error" to solve may be undesirable. (Or not? The harder the better?) But even the term "trial-and-error" is hard to define. Perhaps an adequate working definition would be: "Eliminating a possibility is said to require trial-and-error when the elimination cannot be proven with a single clause of moderate length." With this definition, Antique Bargains at the Hartlan Flea Market does not require trial-and-error, but it is still rather difficult. Especially without the Hint ("Fifth Clue"). If there's interest I'll post a step-by-step solution using neither trial-and-error nor the Hint. Bravo, Angra Mainyu ! I'm afraid to ask whether you found this to be a fun challenge ... or just a tedious annoyance. It was fun, but it was late at night and I expected it to be faster, so in the end it got somewhat longer than I was planning, which did annoy me a bit - but I wasn't going to leave it for later, or read the post with hints no way. It's my fault for not turning it into a problem with some variables and functions and instead resolving it with the names and all. I also have written software to solve puzzles of this sort; I use it to verify the solution and its uniqueness, and to eliminate unnecessary clues. For a while many years ago I composed logic puzzles for Penny Press Logic and Dell Logic. (* - Although their logic puzzle editing styles are very different, these two magazines have the same mailing address and same corporate overlord. — Another example of the American business trend toward consolidation.) If there's sufficient interest I may compose another puzzle to post here. Make it harder? Easier? Based on Liars and Truthers? Thanks for the offer. I find them interesting, but my winter half-vacation (Southern Hemisphere here) ends this Thursday, and I don't know how much time I'll have to solve logic puzzles for fun, if any. So if you post one, I'll tackle it, but I don't know when. As for harder/easier, I'd go with harder (then again, that does take longer), but I don't know what other readers think. Liars and Truthers sounds fun, but this one was fun too and I have no preference there. #### Angra Mainyu ##### Veteran Member Swammerdami said: If there's interest I'll post a step-by-step solution using neither trial-and-error nor the Hint. If you have it already written, yes, thanks, it'll be interesting to see your approach. #### Swammerdami ##### Squadron Leader Staff member Let me show how I solve puzzles of this type. (The cross-hatch grids sometimes presented are generally NOT the best approach.) First I get all the characters in view: Forenames are H/J/K/L/M/N/O Surnames are A/B/C/D/E/F/G Items are knife/mayan/doll/watch/coin/photo/gun Prices are$25/30/40/45/50/60/80
(Notice that I replaced "pistol" with "gun" just so I an use "p" as an unambigious abbreviation should that prove convenient. Similarly, I let "m" define the Mayan wagon instead of the ambiguous "w.")​

Then I convert each Clue to a List of different people/purchase/price combinations. "Mr." and "Miss" imply possible forenames.

Clue 1
--mayans+20
H/J/K/LElwell-s

Clue 2
M/OBrown-t+20
Hank--t
Nancy--u+20
M/ODolliver-u

Clue 3
--watch80/50
--coin60/45 = Larry+15
H/J/K/LFairbanks-60/45 = photo+15
Nancy-80/50
---25/30/40
---25/30/40
---25/30/40

Clue 4
H/J/LCliftongun-
--doll-
Kenneth---
M/N/OGifford--

Some of the facts in the Clues won't lend themselves to easy incorporation into these tables. Make a record of them. In this case there was only one:
• Mary spent more than Olivia. (From Clue 2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now the fun begins! Merge information from the separate tables. (Right away we see from Clues 2 and 4 that Nancy's surname must be Gifford. You can also deduce Nancy's purchase by elimination.) But I won't pursue this further, in case someone else wants to give it a whack!

Continuing on:
• In #3, Fairbanks cannot be $60. (Both photo and coin would be$45 but no price is duplicated.) So he is $45; photo is$30; coin is $60; Larry is$45.
• Nancy Gifford spent $20 more than Dolliver (Clue 2), so not$20 more than Elwewll (no price is duplicated) so isn't mayan (Clue 1) so is knife by elimination.
• By now, we've got most of the gift/price pairings in the Clue 3 box. We can see that mayan ($20 more than Elwell) can only be$45.
Here are the Clue tables as they stand now; information from table #1 has been merged into #3.

Clue 2
M/OBrown-t+20
Hank--t
NancyGiffordknifeu+20
M/ODolliver-u

Clue 3 (and 1)
--watch80/50
--coin60
LarryFairbanksmayan45
NancyGiffordknife80/50
--photo30
H/J/KElwell-25
---40

Clue 4
H/JCliftongun-
--doll-
Kenneth---
NancyGiffordknife-

• Mary spent more than Olivia. (From Clue 2)

We see that the Clue 3 and Clue 4 tables can be merged. Don't forget to eliminate K (Kenneth, not doll) from Elwell during this merge:

Clue 3 (and 1 and 4)
--watch80/50
--coin60
LarryFairbanksmayan45
NancyGiffordknife80/50
--photo30
H/J (not K)Elwelldoll25
H/JCliftongun40

• Hank is $20 less than Brown (Clue 2) so cannot be Elwell (he is$20 less than Fairbanks). Elwell is John; Clifton is Hank by elimination.
• Brown is $20 more than Hank (Clue 2) so is$60.
• Nancy Gifford is $20 more than Dolliver (Clue 2) rather than Brown, so isn't$80.

By now, the information has been gathered into one odd fact
• Mary spent more than Olivia.
and a single table:
All Clues
--watch80
M/O (Mary)Browncoin60
LarryFairbanksmayan45
NancyGiffordknife50
M/O (Olivia)Dolliverphoto30
JohnElwelldoll25
HankCliftongun40

The leftover names (Kenneth Ainsworth) complete the first row.
Q.E.D.