Alien Ages
NAME -------- RACE ----- PLANET -------- AGE
1) Bleep ------- Tartan ----- Parp ---------- 213
2) Ting -------- Polyp ------ Dorb ---------- 385
3) Hoot -------- Bunter -----Esther -------- 706
4) Eek --------- Crispy ----- Booper -------- 503
5) Peep ------- Winky ----- Grunt --------- 897
6) Doodah -----Fodder ---- Flip ------------- 32
Six galactic space people enterred the Funniest Space Face competition. The judges recorded the alien's name, race of origin, home planet, and age for the first six places in the competition. Due to a clerical error, although the info is in the right column, it is not assigned to the correct alien. There is one correct entry in each column. The following facts are true about the correct order:
1. Grunt is one place above Fodder.
2. Booper is three places below Eek, and two below 32.
3. Doodah is two places above Tartan and one below 385.
4. The 706-year old alien is three places above Ting.
5. Peep is two places below Bunter, and one above Parp.
6. Esther is one place above 213, and three above Polyp.
Please assist the judges. Find the correct name, race, planet, and age for each position.
1) Bleep ------- Tartan ----- Parp ---------- 213
2) Ting -------- Polyp ------ Dorb ---------- 385
3) Hoot -------- Bunter -----Esther -------- 706
4) Eek --------- Crispy ----- Booper -------- 503
5) Peep ------- Winky ----- Grunt --------- 897
6) Doodah -----Fodder ---- Flip ------------- 32
Six galactic space people enterred the Funniest Space Face competition. The judges recorded the alien's name, race of origin, home planet, and age for the first six places in the competition. Due to a clerical error, although the info is in the right column, it is not assigned to the correct alien. There is one correct entry in each column. The following facts are true about the correct order:
1. Grunt is one place above Fodder.
2. Booper is three places below Eek, and two below 32.
3. Doodah is two places above Tartan and one below 385.
4. The 706-year old alien is three places above Ting.
5. Peep is two places below Bunter, and one above Parp.
6. Esther is one place above 213, and three above Polyp.
Please assist the judges. Find the correct name, race, planet, and age for each position.
posted by Zaux at
6:16 AM
18 Comments:
I come up with 3 possible arrangements:
X indicates where the left over names, races, planets , #s may be filled in.
Name , Race, Planet, Age
Eek X Grunt 385
Doodah Fodder X 32
X Bunter Esther 706
X Tartan Booper 213
Peep X X X
Ting Polyp Parp X
OR
X X Grunt 706
Eek Fodder X 385
Doodah Bunter Esther 32
Ting X X 213
Peep Tartan Booper X
X Polyp Parp X
OR
Eek X X 385
Doodah Bunter Grunt 32
X Fodder Esther 706
Peep Tartan Booper 213
X X Parp X
Ting Polyp X X
However if all the info about each alien is wrong then no answer exists since Doodah must be 32.
Surely I made a mistake this time.
Cam
Define the items in the first columns as N1 to N6
and the other items by D1 to D6.
i.e. N1 = Bleep, ..., N6 = Doodah etc.,
and D1 is any of Tartan, Parp or 213.
Translate the original info =>
a D5 = D6+1
b D4 = N4-3
c D4 = D6-2
d N6 = D1+2
e N6 = D2-1
f D3 = N2+3
g N5 = D3-2
h N5 = D1+1
i D3 = D1+1
j D3 = D2+3
Bringing Ns to the LHS and rearranging =>
f N2 = D3-3
b N4 = D4+3
g N5 = D3-2
h N5 = D1+1
d N6 = D1+2
e N6 = D2-1
a D5 = D6+1
c D4 = D6-2
i D3 = D1+1
j D3 = D2+3
Use f, b, g and h to find more equations relating the Ds.
g & h => D3-2 = D1+1 => D3 = D1+3
but i=> D3 = D1+2 => D1+2 = D1+3 => 2 = 3
therefore I suspect the given data is wrong
unless someone can see an error in my results.
Hmmm, I notice that Cam has just posted. I'll stick my neck out and post anyway.
At least one of us (Chris, Cam or Zaux) has made a mistake. Please, please, please don't let it be Chris ;)
If not for the contradiction, the rest of the reasoning looked like it was going to be a piece of cake.
I made a small mistake when I wrote "i => D3 = D1+2 ...". It still causes a contradiction though.
re-checked the given ... all correct
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Sorry guys ... I corrected the problem statement to indicate there is one correct entry in each column.
carrying on with my solution, since 1st and 3rd matrix has Esther and Booper correct, then they must be eliminated. 2nd matrix remains.
And we simply fill in the Xs so as to maintain only 1 correct per column.
Answer:
Hoot Crisp Grunt 706
Eek Fodder Flip 385
Doodah Bunter Esther 32
Ting Winky Dorb 213
Peep Tartan Booper 503
Bleep Polyp Parp 897
Cam
I completely misinterpreted the question. I thought that the Planet, Race and Age were correct as a group. I now see that Cam has interpreted it correctly - I wondered what he was up to. The problem now looks quite fiendish. Annoyingly I don't have time before tomorrow evening - but no doubt I'll create some.
No more calls ... we have a winner.
Nice work Cam.
What type problems do you guys like best?
Cam, have you solved Riemann's Hypothesis yet?... heh heh.
Thanks, Zaux.
As far as the problems I like best: the challenging ones
The math and logic categories tend to offer the more challenging puzzles (not to say other categories don't have whoppers).
As far as the Riemann's hypothesis goes, I'll make sure to collect the million bucks before posting the solution here $-) . Finding a counterexample would be perversely more satisfying, as it would suggest that order is merely an illusion @-).
Cam
Hi Zaux. I'll give you a laugh - I had a minor fling at Riemann. I managed to reproduce what I later found out were known as the Stieltjes constants.
I was pretty sure that I was doomed before I started as I knew there was no way to solve a general polynomial of more than the fourth order. In fact I was pretty sure that I was doomed to fail - fullstop :)
There use to be a site, which offered big bucks for fasctoring a composite of 2 primes. The composites were used as security keys. I worked on one for months ... set up a 200 x 200 spreadsheet and attempted to dupicate the multiplication. the one I worked on was 190-some digits long. Was never succesful... but lots of fun. Are you guys familiar with the site? I don't remember the name.
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I found it ... they stopped paying big monetary rewards for factoring huge composites in 2007. It was RSA Labs ...
Alien ages. Descriptive solution. PART1 OF 2
The statements for relating the aliens can be represented graphically:
All statements must fit into a 4x6 table. None can overlap. i.e. no two 1s may occupy the same place on the table
1. Grunt is one place above Fodder.
0010
0100
The first row A, may be 1,2,3,4,5
2. Booper is three places below Eek, and two below 32.
1000
0001
0000
0010
The first row B, may be 1,2,3
3. Doodah is two places above Tartan and one below 385.
0001
1000
0000
0100
The first row C, may be 1,2,3
4. The 706-year old alien is three places above Ting.
0001
0000
0000
1000
The first row D, may be 1,2,3
5. Peep is two places below Bunter, and one above Parp.
0100
0000
1000
0010
The first row E, may be 1,2,3
6. Esther is one place above 213, and three above Polyp.
0010
0001
0000
0100
The first row F, may be 1,2,3
Now, looking at each column we can identify the overlap of 1s with the following inequalities:
*1) B != C+1 != D+3 !=E+2
*2) A+1 != C+3 != E != F+3
*3) A != B+3 != E+3 !=F
*4) B+1 != C != D != F+1
Solve for each letter:
A != (B+3),(C+2), (E-1),(E+3),(F),(F+2)
B !=(A-3),(C-1),(C+1),(D-1),(D+3),(E),(E+2),(F-3),(F)
C!= (A-2), (B-1),(B+1),(D),(D+2),(E+1),(E-3),(F),(F+1)
D!=(B+1),(B-3),(C),(C-2),(E-1),(F+1)
E!=(A-3),(A+1),(B),(B-2),(C-1),(C+3),(D+1),(F-3),(F+3)
F!=(A),(A-2),(B),(B+3),(C-1),(C),(D-1),(E-3),(E+3)
since B,C,D,E,F can only have values 1,2,3 statements of X-3 where X=B,C,D,E,F are trivial, and can be eliminated and X+3 can be eliminated for all but A !=
A != (B+3),(C+2), (E-1),(E+3),(F),(F+2)
B !=(A-3),(C-1),(C+1),(D-1),(E),(E+2),(F)
C!= (A-2), (B-1),(B+1),(D),(D+2),(E+1),(F),(F+1)
D!=(B+1),(B-3),(C),(C-2),(E-1),(F+1)
E!=(A-3),(A+1),(B),(B-2),(C-1),(D+1)
F!=(A),(A-2),(B),(C-1),(C),(D-1)
If F=1
After eliminating inequalities from F
A=2,4,5
B=2,3
C=3
D=1,3
E=1,2,3
After eliminating inequalities for C=3
A=2,4,5
B=3
D=no choices
E=1,3
Thus F !=1
If F=2
After eliminating inequalities from F
A=1,3,5
B=1,3
C=1
D=1,2
E=1,2,3
After eliminating inequalities for C=1
A=1,5
B=1,3
C=1
D=2
E=1,2,3
After eliminating inequalities for D=2
A=1,5
B=3
C=1
D=2
E=1,2
After eliminating inequalities for B=3
A=1,5
B=3
C=1
D=2
E=2
After eliminating inequalities for E=2
A=no choices
B=3
C=1
D=2
E=3
If F=3
After eliminating inequalities from F
A=1,2,4
B=1,2
C=1,2
D=1,2,3
E=1,2,3
Test B=1... eliminate inequalities for B=1
A=1,2
B=1
C=1
D=1,3
E=2,3
After eliminating inequalities from C=1
A=1,2
B=1
C=1
D=3
E=2,3
After eliminating inequalities from D=3
A=1,2
B=1
C=1
D=3
E=2,3
Test A=1... eliminate inequalities for A=1
A=1
B=1
C=1
D=3
E=3
So A=1,B=1,C=1,D=3,E=3,F=3 does not cause an inequality to occur
Go back and test A=2... eliminate inequalities forA=2
A=2
B=1
C=1
D=3
E=2
So A=2,B=1,C=1,D=3,E=2,F=3 does not cause an inequality to occur
Now go back and test B=2, eliminate all the B=2 inequalities
A=1,2,4
B=2
C=2
D=1,2
E=1,3
eliminate all the C=2 inequalities
A=1,2
B=2
C=2
D=1
E=3
eliminate all the E=3 inequalities
A=1
B=2
C=2
D=1
E=3
So A=1,B=2,C=2,D=1,E=3,F=3 does not cause an inequality to occur
Cam
PART 2 OF 2
This leaves 3 possible choices to choose from.
A=1,B=1,C=1,D=3,E=3,F=3
A=1,B=2,C=2,D=1,E=3,F=3
A=2,B=1,C=1,D=3,E=2,F=3
These translate into :
Name , Race, Planet, Age
Eek X Grunt 385
Doodah Fodder X 32
X Bunter Esther 706
X Tartan Booper 213
Peep X X X
Ting Polyp Parp X
OR
X X Grunt 706
Eek Fodder X 385
Doodah Bunter Esther 32
Ting X X 213
Peep Tartan Booper X
X Polyp Parp X
OR
Eek X X 385
Doodah Bunter Grunt 32
X Fodder Esther 706
Peep Tartan Booper 213
X X Parp X
Ting Polyp X X
We are told only statement per column is correct. Since 1st and 3rd matrix has Esther and Booper correct, then they must be eliminated. 2nd matrix remains.
And we simply fill in the Xs so as to maintain only 1 correct per column.
Answer:
Hoot Crisp Grunt 706
Eek Fodder Flip 385
Doodah Bunter Esther 32
Ting Winky Dorb 213
Peep Tartan Booper 503
Bleep Polyp Parp 897
Cam
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