[Day 5] Ice Cream Explosion

[HerrZynisch]

This problem is cursory of creed so ask him for the solution!

Ice Cream!!!!
Warning: Your head may explode if you try to solve this problem.
Problem solving isn't just for IMSA students! Six logical friends { Arlen, Boris, Cecil, Doran,
Edith, and Frank { having just nished some pretty hairy logic problems, decided to go to
Wacky Jack's Primo Ice Cream Emporium to celebrate. Each ordered their ice cream in a
wae cone or a dish, except for the one who ordered the Slurp-A-Licious Bucket-O-Yum{
a delectable concoction with two scoops each of Jack's ve Specialty Flavors { in which
case it came in a commemorative Wacky Jack Bucket (which you got to keep if you ate it
all). From the following clues, can you decide who ordered what? Note: All solvers made
their selections from Jack's ve Specialty Flavors: Blueberry Farkle, Chocolate Smudge,
Marshmallow Whoop, Pecan Passion, and Peppermint Blast. For the cones, you must spec-
ify the order of the scoops.

1. No cone had more than three scoops of ice cream, and no dish had more than ve.
2. Except for the problem solver who got the Slurp-A-Licious Bucket-O-Yum, no one got
more than one scoop of the same
avor.
3. The number of scoops in Edith's dish was the same as the sum of the numbers of
scoops in Arlen's and Cecil's cones.
4. Cecil and Edith together had the same number of scoops as Arlen and Frank together.
5. If Frank had an even number of scoops, then there were 23 scoops among the six
solvers.
6. If Frank had an odd number of scoops, then there were 25 scoops among the six solvers.
7. If Boris had an odd number of scoops, then Edith had an even number.
8. Boris had fewer scoops than Doran.
9. Exactly two solvers had exactly three scoops of ice cream.
10. Frank ordered a dish if and only if Boris ordered a cone.
11. Arlen had three scoops of ice cream if and only if no two cones had the same number
of scoops.
12. Exactly four solvers had Marshmallow Whoop, exactly four had Pecan Passion, and
exactly two had both.
13. Either Arlen's
avors were a subset of Edith's, or Frank's were a subset of Cecil's.
14. Frank did not order Pecan Passion, and Cecil did not order Marshmallow Whoop.
15. If Cecil ordered just one scoop, then Arlen ordered Pecan Passion.
16. Boris and Doran were the only two to order Peppermint Blast.
17. Arlen and Frank had no
avors in common if and only if Boris and Frank had exactly
one
avor in common.
18. Two cones had a scoop of Chocolate Smudge second from the top.
19. Frank had exactly two scoops if and only if Pecan Passion was always the bottom scoop
of the cone it was on.

[clementine]

I think Hints #1, 2, and 17 got cut off a bit. I think it only really matters in number 1 that we can't read what number it's saying at the end.

[Nick]

Replace the names:
Arlen = A
Boris = B
Cecil = C
Doran = D
Edith = E
Frank = F

Current results:

1. No cone had more than three scoops of ice cream, and no dish had more than five.
3. The number of scoops in Edith's dish was the same as the sum of the numbers of scoops in Arlen's and Cecil's cones.
4. Cecil and Edith together had the same number of scoops as Arlen and Frank together.
8. Boris had fewer scoops than Doran.

Bucket = 10 scoops
Dish =< 5 scoops
Cone =< 3 scoops

A = cone
C = cone
E = dish
F = 2C =< 6 =/= bucket
B < D
D > B = bucket

------

5. If Frank had an even number of scoops, then there were 23 scoops among the six solvers
6. If Frank had an odd number of scoops, then there were 25 scoops among the six solvers.

But F = 2C = {even}
For all six is 23
But bucket is 10
For remaining five is 13

------

7. If Boris had an odd number of scoops, then Edith had an even number.

A + F = C + E
thus
A + C + E + F = {even}
but
(A + C + E + F) + B = 13 = {odd}
thus
B = {odd}
thus
E = {even}

------

9. Exactly two solvers had exactly three scoops of ice cream.

A + F = C + E
E and F are even
thus
A and C are both even or odd

B is odd and D is even
and
there are at least 2 odd number
thus
A or C must be odd
A and C are odd

E = {even} =< 5 = A + C
A = {odd} =< 3
C = {odd} =< 3
thus
A and C cannot be both 3
A or C must be 1 or 3 and E must be 4
B must be 3

(A + C) + E + F + B = 13
4 + 4 + F + 3 = 13
F = 2

------

2. Except for the problem solver who got the Slurp-A-Licious Bucket-O-Yum, no one got more than one scoop of the same flavor.
13. Either Arlen's flavors were a subset of Edith's, or Frank's were a subset of Cecil's.

D = {2a, 2b, 2c, 2d, 2e}

E = A + C
thus
E > A
A can be subset of E

F = 2C
F > C
F cannot be subset of C

Answer: A subset of E

------

Fact
12. Exactly four solvers had Marshmallow Whoop, exactly four had Pecan Passion, and exactly two had both.
14. Frank did not order Pecan Passion, and Cecil did not order Marshmallow Whoop.
16. Boris and Doran were the only two to order Peppermint Blast.
18. Two cones had a scoop of Chocolate Smudge second from the top.
19. Frank had exactly two scoops if and only if Pecan Passion was always the bottom scoop of the cone it was on.

Variables
10. Frank ordered a dish if and only if Boris ordered a cone.
11. Arlen had three scoops of ice cream if and only if no two cones had the same number of scoops.
15. If Cecil ordered just one scoop, then Arlen ordered Pecan Passion.
17. Arlen and Frank had no flavors in common if and only if Boris and Frank had exactly one flavor in common.

[Bluejay]

I think Hints #1, 2, and 17 got cut off a bit. I think it only really matters in number 1 that we can't read what number it's saying at the end.

I'm guessing that number at the end is five?

[JSaint]

I failed discreet mathematics for a reason

1. Cone <=3 dish <=5
2. Everyone else + 2 =total
3. E dish scoops = A cone scoops + C cone scoops
4. C scoops + E scoops = A scoops + F scroops
5. If F = even then total= 23
6. If F = odd then total =25
7. If B = odd E = even
8. B scoops < D scoops
9. B = cone then F = dish else F = Cone
11 A = 3 if twocones scoops not equal
12. 2 solvers had Marshmallow whoops and Pecan Passion 2 had just MW 2 had just pecan
13. flavours repeat for A and E or flavours repeat for F & C
14. F Flavour != Pecan and C Flavour != MW
15 IF C =1 then A = Pecan Passion
16. B and D = Peppermint Blast
17. A and F Not subset of N amd F had pme
18. Two cones 2nd Flavour = choco smudge
19. F Scoops = 2 IIF PP = Bottom scoop for all cones

A(cone) B C(cone) D E(dish) F
2 5 5 2 2C


E scoops = A + C scoops
C + E scoops = A scoops + F Scoops
C + A + C = A scoops + F scoops

F scoops(always even no matter what) = 2C Scoops

Therfore forumla is

Total + 2 = 23
A+C = E

2E + 2 + B = 23

Guessing that

2E + 2 + 1 = 23

2E cannot be 10 because all there are cones in one variant. Logically impossible

Formula as of now is

2E + B + D + F = 23 ... needs to be grouped up and simplified.

It is possible that the A + C cone variants add up to exactly 5 in a 3+2 combo

Giving us

10 + 4(F which is 2C) + 5 (D) +4(B)

Again this is just guess work at this point...

So

3(A) + 4 (B) + 2(C) + 5 (D) + 5(E) + 4 (F) = 23

Wrong Premise where I thought A = C= D =F
----
X is even

4X + 2 + B = 23 or 4x + 2 + D =23

X is odd

4x + 2 + D =25 or 4x + 2 + B =25

B < D so B =1 D =2(bucket base) or B = 2(Bucket case) 3 <= D < 5

A = C based on 4 so therfore A<=2
X = 1,2

8 + 2 +D =25 impossible!

Wha happens if the 2 constant for the bucket was in the X list?

[Nick]

A = cone = b(pecan,choco,blue)t
B = dish = (pepper,marsh,choco)
C = cone = (pecan)
E = dish = (pecan,choco,marsh,blue)
F = cone = b(marsh,choco)t

[JSaint]

Your solution is wrong? Because I am wrong and the bucket contains 10 scoops of icecream corresponding to all the flavours and 2 each

5x2... your solution has a total of 12 flavours which adds up to 22. so not quite right.

[Nick]

Your solution is wrong? Because I am wrong and the bucket contains 10 scoops of icecream corresponding to all the flavours and 2 each

5x2... your solution has a total of 12 flavours which adds up to 22. so not quite right.

A = 3
B = 3
C = 1
D = 10
E = 4
F = 2
Total = 23

[JSaint]

I concede defeat to the Nick.

I am just a linguistically inclined dev good at finding patterns and reusing code and writing less ^^.

You mayz has bucketz...

I will just have cup... and whoever else commented can have cones ^^