This is a slide show to explain in detail how to solve
a puzzle of a common sort. Use the right arrow key
to go to the next step and left arrow keys to go to
the last step. To terminate before the end, hit the
Escape key. Ready? Hit the right arrow key.
High in the m ountains of a wild ernes s pa rk, four backpa ckers h appe ned
to meet at the same ca mpsi te, wh ere they al l sp ent the nigh t. On e ma n
was from Bi llin gs. From the sta teme nts belo w, determin e th e ho me
town of e ach man and the co lor o f hi s ba ckpack.
1. Larry h ad a fire mad e be fore the man from Tucson and the fell ow
with the blue pack arrived. Kevin cam e even later.
2. Both Perry an d th e ma n fro m San Fran cis co said it wa s th eir first
trip to this spo t. The man wi th the re d pa ck sai d he had bee n th ere
twice be fore.
3. The man from L.A. ga ve Fred and the pers on with th e gre en p ack
som e mo leskin for their blis tered fee t. "No ne for me , th anks," s aid
Kevin, "It's m y back that hurts ."
4. "I b elie ve I've travel led the farth est to g et h ere," said the man
with the orang e pa ck. "No," Fred repli ed, "I th ink Kevin did."
To solve this problem, we should try to find a way to organize the information so that
drawing inferences is easy or even mechanical. Let us set up some tables to represent all
of the important features of the problem. Hit the right arrow key to continue.
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Larry
Perry
Fred
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
With these we will be able to keep track of the information without having the puzzle set
up in front of us. If we find, for instance that Larry came from L.A., then we’ll put an ‘X’ in
the square that goes down the ‘Larry’ column and across the ‘L.A.’ row. If we find that
Larry is not from L.A., then we’ll put a “~” in that square. Hit the right arrow key to
continue.
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Larry
Perry
Fred
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
Let’s take statement number one and see what we can infer from it. It seems that Larry
cannot be from Tucson or have blue pack, for no one can make a fire in a place before
they arrive at that place. Furthermore Kevin must also be different from the man from
Tucson and not have a blue pack. So let us put the appropriate marks in the squares to
note these 4 facts. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
~
~
~
~
Larry
Perry
Fred
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
Larry is not from Tucson and Larry doesn’t have a blue pack and Kevin is not from Tucson and
Kevin does not have a blue pack. These 4 pieces of information account for the 4 tildes in the
boxes. But there is something else we may be able to infer from 1. It doesn’t strictly follow but
the problem cannot be done without inferring something from the context. The man from Tucson
is not identical to the man with the blue pack. A logician would not talk this way so let us assume
that the writer of the puzzle was not a logician. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
~
~
~
~
Larry
Perry
Fred
blue
~
orange
red
green
Billings
San Fran
L.A.
Tucson
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
So we put a ‘~’ in the Tucson/blue square. Now let’s take the second statement and
proceed in the same way. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
~
~
~
~
Larry
Perry
Fred
blue
~
orange
red
green
Billings
San Fran
L.A.
Tucson
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
Using the same sort of logic we can tell that Perry is not from San Fran and the man with
the red pack is not Perry or from San Fran. So let’s mark those 3 squares with tildes. Hit
the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
~
~
~
~
~
~
green
Billings
San Fran
L.A.
Tucson
~
Larry
Perry
Fred
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
Perry is not from San Fran and the man with the red pack is not Perry or from San Fran.
Now let’s consider the 3rd statement. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
~
~
~
~
~
~
green
Billings
San Fran
L.A.
Tucson
~
Larry
Perry
Fred
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
From #3 we see that Fred is not from L.A., Fred does not have a green pack and the Man
from L.A. does not have a green pack. Furthermore Kevin is not from L.A. or have a green
pack. Let’s fill in the squares with tildes. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
green
~
~
~
~
~
~
~
~
~
Billings
San Fran
L.A.
Tucson
~
Larry
Perry
~
~
Fred
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
That’s why we got 5 new tildes (in red). Now let’s consider statement #4 Hit the right
arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
green
~
~
~
~
~
~
~
~
~
Billings
San Fran
L.A.
Tucson
~
Larry
Perry
~
~
Fred
Kevin
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
What can we infer from 4? That Fred and Kevin do not have an orange pack. Let’s put in
those two new tildes. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
green
~
~
~
~
~
~
~
~
~
~
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
~
Larry
Perry
High in the moun tain s of a wil derne ss p ark, fou r backp ackers happ ened
to mee t at the sam e camps ite, where they a ll s pent the nig ht. One m an
was from Billi ngs. Fro m th e statem ents bel ow, de termi ne the h ome
to wn of each ma n an d th e color of h is b ackpack.
1. La rry had a fi re ma de b efore the man from Tucson and the fel low
with the blu e pa ck arrived . Kevin ca me e ve n la ter.
2. Both Perry a nd the m an from Sa n Fra nci sco sai d it was their first
tri p to thi s sp ot. The man with the red p ack sa id h e ha d be en there
twice b efore .
3. Th e ma n fro m L.A. g ave Fre d an d th e pe rson wi th the g reen pack
so me m oles kin for thei r bli stere d fe et. "None for m e, thanks," said
Kevin , "It's my back that hurts."
4. "I beli eve I've tra ve lled the farthest to get here," sai d th e ma n
with the oran ge p ack. "No," Fred repl ied, "I think Kevin did ."
Fred and Kevin do not have an orange pack. So we got 2 new tildes (in red). We now
have captured all of the important information in the boxes. We can get rid of the
statement of the original puzzle and see what we can reason. Do you see any way to
make inferences. Think about it before you hit the right arrow key.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
green
~
~
~
~
~
~
~
~
~
~
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
~
Larry
Perry
At this point I will introduce a couple of useful principles. First of all, (Principle 1), if you
have all but one square in a row or column filled with tildes, then the empty square should
get an ‘X’. Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
~
~
~
~
~
~
~
X
~
Fred
Kevin
~
~
Perry
red
green
~
~
Larry
orange
~
~
Billings
San Fran
L.A.
Tucson
So since Kevin does not have a blue or orange or green backpack, we’ve inferred that
Kevin has a red backpack. But if Kevin has the red backpack then the other guys don’t
have that color pack. So the second principle is that if you have an ‘X’ in a row or column
then tildes go in all the other squares of that row or that column. Imagine how we will do
that and then hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
orange
red
green
~
~
~
~
~
~
~
~
~
Larry
Perry
Fred
~
~
~
~
X
~
Kevin
~
~
Billings
San Fran
L.A.
Tucson
We only got two new tildes because one tilde was already on that row. Note that because
of one of those tildes we now have 3 tildes on another column. So we can put in another
‘X’, Find it before you hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
~
~
~
Larry
Perry
red
green
~
~
~
orange
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
And this new ‘X’ mark lets us fill in one more tilde. Let’s do that. Hit the right arrow key to
continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
~
~
~
~
Larry
Perry
red
green
~
~
~
orange
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
Before we can continue we need at least one (or two more principles). There are no more
‘X’s or ‘~” to be made from our first two principles. So consider this: If Fred is identical to
the man with a blue pack and the man with the blue pack is not from Tucson (both facts
seen above), then what can we infer? Hit the right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
~
~
~
~
~
Larry
Perry
orange
red
green
~
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
If Fred is identical to the man with a blue pack and the man with the blue pack is not from
Tucson then Fred is not from Tucson (red tilde above). The general principle is if a is
identical to b and b is not identical to c then a is not identical to c. We can also see that if
a=b and b=c then a does = c. So these two (or one) principles are enough with the others
to solve the rest of this puzzle. There are many ways to go at this point, but let’s follow
what we just created. Note the new tilde allows another inference. Think and then hit the
right arrow key to continue.
Larry
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Perry
Fred
Kevin
blue
~
~
X
~
~
~
~
Larry
Perry
orange
red
green
~
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
We get a new ‘X’ from the three on the same row tildes, This ‘X’ allows us to fill in more
tildes. Let’s do that. Hit the right arrow key to continue.
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Larry
Perry
~
~
~
~
X
~
~
~
~
Larry
Perry
Fred
Kevin
blue
orange
red
green
~
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
The L.A./Perry tilde allows us to see who is from L.A. i.e. Larry; Let’s fill in that new X. Hit
the right arrow key to continue.
Billings
San Fran
L.A.
Tucson
blue
orange
red
green
Larry
Perry
X
~
~
~
~
X
~
~
~
~
Larry
Perry
Fred
Kevin
blue
orange
red
green
~
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
If Larry is from L.A. then he is not from San Fran or Billings (Using principles 1 and 2 for
the next step.) Let’s fill in the two new tildes. Hit the right arrow key to continue.
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
~
~
~
Larry
Perry
Fred
Kevin
blue
orange
red
green
~
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
Again there are many ways to go. Not with principles one and two but with the identity
principles. We have 3 X’s that we have not explored with the identity principles yet. What
can we infer from the Larry/L.A. ‘X’? Think before you hit the right arrow key to continue.
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
~
~
~
Larry
Perry
Fred
Kevin
blue
orange
red
green
~
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
~
~
Billings
San Fran
L.A.
Tucson
What can we infer from the Larry/L.A. ‘X’? We can infer that if Larry is the guy from L.A.
and Larry does not have the blue or red backpack then the guy from L.A. doesn’t have an
blue or red backpack. Furthermore, since Larry is from L.A. and the guy from L.A. does
not have a green backpack then Larry does not have a green backpack. Three more ‘~’s.
Think before you hit the right arrow key to continue.
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
~
~
~
~
Larry
Perry
Fred
Kevin
~
~
~
~
X
~
~
~
~
~
X
~
Fred
Kevin
blue
~
~
orange
red
~
~
green
~
Billings
San Fran
L.A.
Tucson
One of those three tildes allow us to complete the bottom rectangle. We can fill it in using
principles 1 and 2 Think before you hit the right arrow key to continue.
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
~
~
~
Larry
Fred
Kevin
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Perry
Fred
Kevin
blue
orange
~
~
Hit the right arrow key to continue.
red
~
~
green
~
Billings
San Fran
L.A.
Tucson
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
~
~
Hit the right arrow key to continue.
red
~
~
green
~
Billings
San Fran
L.A.
Tucson
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
~
~
orange
red
~
~
green
~
Billings
San Fran
L.A.
Tucson
The color versus hometown rectangle deserves an ‘X’ by principle 1 leading to two ‘~’s by
principle 2. Imagine and hit the right arrow key to continue.
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
~
~
Hit the right arrow key to continue.
X
red
~
~
green
~
Billings
San Fran
L.A.
Tucson
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
~
~
~
~
X
~
red
~
~
green
~
Billings
San Fran
L.A.
Tucson
Again it looks like we might want to use principles 3 and 4. What could be useful? How
about this: We see Kevin with a red backpack and Kevin is not from Tucson, so the guy
with a red backpack is not from Tucson. Let’s put in that ‘~’. Hit the right arrow key to
continue.
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
~
~
~
~
X
~
red
~
~
~
green
~
Billings
San Fran
L.A.
Tucson
Now it looks like we can fill in the color versus hometown rectangle with principles one
and 2. Hit the right arrow key to continue.
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
~
~
~
~
X
~
Hit the right arrow key to continue.
red
~
~
~
green
~
X
Billings
San Fran
L.A.
Tucson
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
~
~
~
~
X
~
Hit the right arrow key to continue.
red
green
~
~
~
~
~
~
X
Billings
San Fran
L.A.
Tucson
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
blue
orange
X
~
~
~
~
X
~
Hit the right arrow key to continue.
red
green
~
~
~
~
~
~
X
Billings
San Fran
L.A.
Tucson
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
X
~
~
Larry
Fred
Kevin
blue
orange
~
~
~
~
~
X
~
~
~
~
X
~
~
~
~
X
X
~
~
~
~
~
X
~
Perry
Fred
Kevin
Hit the right arrow key to continue.
red
green
~
~
~
~
~
~
X
Billings
San Fran
L.A.
Tucson
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
X
~
~
Larry
Fred
Kevin
blue
orange
red
green
~
~
~
~
~
X
~
~
~
~
X
~
X
~
~
~
~
~
~
X
~
~
~
X
X
~
~
~
~
~
X
~
Perry
Fred
Kevin
Hit the right arrow key to continue.
Billings
San Fran
L.A.
Tucson
Larry
Perry
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
blue
orange
red
green
~
X
~
~
Larry
Fred
Kevin
blue
orange
red
green
~
~
~
~
~
X
~
~
~
~
X
~
X
~
~
~
~
~
~
X
~
~
~
X
X
~
~
~
~
~
X
~
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
Now we can use principle #4. Kevin has a red backpack and the man with the red
backpack is from Billings, thus, Kevin is from Billings. Let’s put in that ‘X’. Hit the right
arrow key to continue.
Larry
Perry
Fred
Kevin
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
X
~
X
~
~
~
~
X
~
X
~
~
~
~
~
~
X
~
~
~
~
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
That ‘X’ allows us to put in two ‘~’, so let’s do that. Hit the right arrow key to continue.
Larry
Perry
Fred
Kevin
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
~
~
X
~
~
~
~
X
~
~
~
~
X
~
X
~
~
~
~
~
~
X
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
And those tildes tell us about the last square. Hit the right arrow key to continue.
Larry
Perry
Fred
Kevin
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
X
~
~
X
~
~
~
~
X
~
~
~
~
X
~
X
~
~
~
~
~
~
X
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
Billings
San Fran
L.A.
Tucson
So we have the complete description spelled out in tabular from. It says
1: Larry is from L.A. and has an orange backpack.
2: Perry is from Tucson and has a green backpack.
3: Fred is from San Fran and has a blue backpack.
4: Kevin is from Billings and has a red backpack.
The first statement ‘Larry is from L.A. and has an orange backpack’. Makes 3 identity
claims: Larry is from L.A., Larry has an orange backpack and the guy from L.A. has an
orange backpack. To check your answer you would want to look in all three of those
corresponding squares. You could also check statements 1 and 4 above against the
original statement of the puzzle to make sure it is consistent with this answer. Hit the
right arrow key to continue.
Larry
Perry
Fred
Kevin
blue
orange
red
green
Billings
San Fran
L.A.
Tucson
~
~
X
~
~
~
~
X
~
X
~
~
X
~
~
~
~
X
~
~
~
~
X
~
X
~
~
~
~
~
~
X
blue
orange
red
green
~
X
~
~
~
~
~
X
X
~
~
~
~
~
X
~
Larry
Perry
Fred
Kevin
That’s all folks.
Hit the right arrow key to end.
Billings
San Fran
L.A.
Tucson