Ice cream toppings

anna_gg · 2016-01-12 09:02:18

The answer is 14, I have represented each topping with a letter; so we have letters A B C D E F G H I J K L M and N, but I am trying to find the 14 possible combinations (with maximum 1 letter in common) and I still can't!!

bobbym · 2016-01-12 12:22:23

Hi;

The best I can do is now 13.

phrontister · 2016-01-12 15:29:34

Got 14...finally!!

That seems to be the max - but that's what I thought when I got 10...and then when I got 11...and then when I got 12...and then when I got 13!

EDIT: Oh no! Blundered! Back to 13 cones.

Last edited by phrontister (2016-01-13 03:55:48)

bobbym · 2016-01-12 16:11:22

Code please.

phrontister · 2016-01-12 16:51:36

Hi Bobby,

Do you mean the code I used to solve it?

I did it by hand, systematically. Getting the 14th was a bit tricky.

EDIT: See post #28. Back to 13 cones.

Last edited by phrontister (2016-01-13 03:57:22)

bobbym · 2016-01-12 17:10:45

That is good! I got 13 using M!

phrontister · 2016-01-12 18:03:27

M!! Didn't think to go there...and I'd be at it all year if I did!

bobbym · 2016-01-12 19:51:26

It took me a long time to write a very slow and inferior program.

phrontister · 2016-01-12 20:56:03

My 'by hand' method took about 3 goes at it to find the system that worked. All three solved 10 cones, but only with the third could I progress further.

I solved the first 10 cones in three groups (cones 1-4, cones 5-7 and cones 8-10) with the 'system that worked'.

Cones 11-13 were solved as a group, using a differently ordered, 90° clockwise version of the 'system that worked' (see my solution in post #30).

The 14th eluded me until I'd had a nice Vittoria Espresso latte, with one sugar.

Last edited by phrontister (2016-01-13 02:56:56)

bobbym · 2016-01-12 21:20:18

Imagine what you would have accomplished on several sugars!

phrontister · 2016-01-12 21:24:23

An M solution afore th' end o' th' year, nae doot!

Last edited by phrontister (2016-01-13 00:38:13)

anna_gg · 2016-01-13 03:01:29

@Phrontister: DABC with ABCN have 3 toppings in common, which, unfortunately, is not allowed
I am stuck in the 13 combinations, although I am sure that the correct answer is 14.

BTW, and sorry to sound like an idiot, what is "M"???

phrontister · 2016-01-13 03:32:59

Oops! How did I miss THAT! >blush<

Back to the drawing board!

"M" = Mathematica.

Too many letters for us 1(2?)-finger typists, hence the abbrevn. Other abbrevs exist too: eg, LB for LibertyBASIC (also way too long).

There are several (well, one at least) older forum members whose typing longevity can be extended through this tactic before it's too late: ie, before they're reduced to typing with the knuckles on their worn-down fingers.

bobbym · 2016-01-13 03:52:47

I am sorry I did not see that.

phrontister · 2016-01-13 04:18:38

In my 'solution' I'd deliberately refrained from using the N in case that might come in handy at the end.

The N appears in the 'solution' in cone 1, but initially it was a D, which gave 13 solved cones.

My idea was to try to use the N via a strategic placement after I'd solved the 13th cone, and I thought I'd found it by:
1. replacing cone 1's D with the N;
2. using {N,D} in the 14th cone;
3. finding two valid toppings for the two vacant places.

But the two toppings I chose don't fit, and I can't find two that do.

Grrrr...

Last edited by phrontister (2016-01-13 04:30:56)

phrontister · 2016-01-13 22:04:34

Hi! Solved it!

I scrapped my previous method as I couldn't get anywhere with it, and went for a fresh approach.

Each row consists of the 14 letters in ascending consecutive alphabetical order, looped for rows that don't start with A.

Rows start with the next successful letter in the alphabet following the previous row's starting letter.

Testing went like this:-

Row 1: A
Row 2: B...obviously no rule breach there.
Row 3:
(a) C breaches the rule in cones {1,2}.
(b) D has no breaches with previous rows, but all of row 4's starting letter options lead to a rule breach.
(c) Tried E next.
Row 4:
(a) F breaches the rule in cones {1,2}.
(b) G works!

All 14 letters are used 4 times each.

Last edited by phrontister (2017-02-26 23:27:34)

bobbym · 2016-01-13 22:33:19

Nice diagram!

phrontister · 2016-01-13 22:37:25

Thanks...Excel. Visual help to quickly find the four locations of any of the 14 toppings.

Last edited by phrontister (2016-01-14 00:58:17)

anna_gg · 2016-01-14 02:34:24

Great job!

phrontister · 2016-01-14 03:05:51

Nice puzzle - thanks for posting it!

phrontister · 2016-01-14 12:56:45

I improved the solving explanation in post #41.

phrontister · 2016-01-14 14:27:33

Found another solution with the post #41 method:

I guess there are other solutions too, and other methods.

EDIT: No, that's not another solution...it's just a rearrangement of the rows, further camouflaged by use of different letters: Solution 1's rows {1,2,3,4} = Solution 2's rows {3,4,1,2}.

Last edited by phrontister (2017-02-26 23:26:58)

Math Is Fun Forum

#26 2016-01-12 09:02:18

Re: Ice cream toppings

#27 2016-01-12 12:22:23

Re: Ice cream toppings

#28 2016-01-12 15:29:34

Re: Ice cream toppings

#29 2016-01-12 16:11:22

Re: Ice cream toppings

#30 2016-01-12 16:51:36

Re: Ice cream toppings

#31 2016-01-12 17:10:45

Re: Ice cream toppings

#32 2016-01-12 18:03:27

Re: Ice cream toppings

#33 2016-01-12 19:51:26

Re: Ice cream toppings

#34 2016-01-12 20:56:03

Re: Ice cream toppings

#35 2016-01-12 21:20:18

Re: Ice cream toppings

#36 2016-01-12 21:24:23

Re: Ice cream toppings

#37 2016-01-13 03:01:29

Re: Ice cream toppings

#38 2016-01-13 03:32:59

Re: Ice cream toppings

#39 2016-01-13 03:52:47

Re: Ice cream toppings

#40 2016-01-13 04:18:38

Re: Ice cream toppings

#41 2016-01-13 22:04:34

Re: Ice cream toppings

#42 2016-01-13 22:33:19

Re: Ice cream toppings

#43 2016-01-13 22:37:25

Re: Ice cream toppings

#44 2016-01-14 02:34:24

Re: Ice cream toppings

#45 2016-01-14 03:05:51

Re: Ice cream toppings

#46 2016-01-14 12:56:45

Re: Ice cream toppings

#47 2016-01-14 14:27:33

Re: Ice cream toppings

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