Ice cream toppings

anna_gg · 2016-01-04 01:45:15

An ice cream parlor has 14 different ice cream toppings. How many ice cream cones can we make, provided that we must place exactly 4 different toppings on each and also the cones must have at maximum one common topping with each other?

bobbym · 2016-01-04 04:33:55

Does the order of the toppings count? For instance, chocolate, sherbert, vanilla, strawberry as opposed to strawberry, chocolate, vanilla, sherbert.

Agnishom · 2016-01-04 04:40:21

Please take me to the parlor

bobbym · 2016-01-04 08:47:17

I do not know where it is and besides ice cream is bad for your teeth.

anna_gg · 2016-01-04 09:08:11

No, order does not count.

bobbym wrote:

Does the order of the toppings count? For instance, chocolate, sherbert, vanilla, strawberry as opposed to strawberry, chocolate, vanilla, sherbert.

anna_gg · 2016-01-04 09:09:17

Let alone with 4 toppings!!

bobbym wrote:

I do not know where it is and besides ice cream is bad for your teeth.

Agnishom · 2016-01-04 12:16:15

[ignore this post]

Last edited by Agnishom (2016-01-04 13:26:20)

bobbym · 2016-01-04 13:13:33

Does that handle the last condition?

Agnishom · 2016-01-04 13:26:36

Nope. I did not see that.

bobbym · 2016-01-04 13:31:50

It is a bit tougher but see if you can come up with an answer.

Relentless · 2016-01-04 15:12:00

Isn't the case where they have exactly one topping in common, just fourteen divided by 3, rounded down? And the case where they have no toppings in common, fourteen divided by four, rounded down? Since none of the four or three remaining toppings can appear twice. Or have I misinterpreted something? Since I guess it is supposed to be more difficult

Last edited by Relentless (2016-01-04 15:13:48)

anna_gg · 2016-01-04 20:24:23

Just to clarify, there is an adequate quantity of each topping & ice cream and also infinite number of cones! (blood sugar levels skyrocket...)

Agnishom · 2016-01-06 03:49:42

bobbym wrote:

It is a bit tougher but see if you can come up with an answer.

I wish I could but I do not understand the question

Relentless · 2016-01-06 04:19:47

I am not sure either. It occurs to me that the "maximum one common topping" means that all of the ice cream cones must have unique toppings, except for one topping which may appear on several cones. But then the problem is simple; the answer is merely four cones with at least three sharing a topping (one topping unused if they all share one), and I don't think this is right.

Can anyone elaborate on the last condition or illustrate it with an example?

Last edited by Relentless (2016-01-06 04:23:18)

anna_gg · 2016-01-06 05:08:45

OK maybe I did not express it properly (sorry, english is not my native language):
Let's say we have infinite quantity of ice cream and cones and various toppings, also in adequate quantity each.
Let's name them T1, T2, T3... T14. One cone can have for example T1, T2, T5 and T12. Another can have T1, T3, T4 and T8 and another T2, T3, T9 and T11...
...and so on.

In other words, any two cones of ice cream cannot have more than one topping in common.

Last edited by anna_gg (2016-01-06 05:46:58)

bobbym · 2016-01-06 06:51:39

Hi;

I think I understand the question but am having some difficulty in solving it.

Relentless · 2016-01-06 14:52:47

Hi - can you explain it? I am still not sure what is allowed.

Edit: So more than one topping can be repeated, but no topping can be repeated more than once? I will think on it and see if I get anywhere at all (:

Last edited by Relentless (2016-01-06 19:06:19)

anna_gg · 2016-01-06 21:22:35

I am trying to think of some other wording to help you understand Maybe the word "toppings" is confusing.
We have, for example:
1. Caramel sauce
2. M&Ms
3. Hot Fudge
4. Peanut butter
5. Oreo
6. Whipped cream
7. Strawberry sauce
...
and so on (14 different ingredients)
Each cone must have 4 of the above toppings (for example, Oreo, Strawberry sauce, Caramel Sauce and Peanut butter) but between ANY TWO ice-cream cones we cannot have more than ONE topping in common.

Relentless · 2016-01-06 21:34:09

Thank you, I think I understand (: Sorry for my confusion!

bobbym · 2016-01-07 22:27:25

It seems there are different answers for different first selections. The largest number of cones I can find so far is 12. This seems small.

anna_gg · 2016-01-08 00:29:55

This is similar to the car plates problem, that must differ by one or two digits etc. I don't think I can solve that one either

bobbym · 2016-01-08 08:27:22

The last bit,

also the cones must have at maximum one common topping with each other?

is what makes the answer so short.

What is this license problem?

Agnishom · 2016-01-08 16:20:33

anna_gg wrote:

I am trying to think of some other wording to help you understand Maybe the word "toppings" is confusing.
We have, for example:
1. Caramel sauce
2. M&Ms
3. Hot Fudge
4. Peanut butter
5. Oreo
6. Whipped cream
7. Strawberry sauce
...
and so on (14 different ingredients)
Each cone must have 4 of the above toppings (for example, Oreo, Strawberry sauce, Caramel Sauce and Peanut butter) but between ANY TWO ice-cream cones we cannot have more than ONE topping in common.

Please take me there

anna_gg · 2016-01-12 08:05:40

bobbym wrote:

The last bit,
also the cones must have at maximum one common topping with each other?
is what makes the answer so short.
What is this license problem?

The license problem is the following (with several variations):
In Riddleland, the license plates are composed of 8 digits, each from 0 to 9. All plates must differ from each other in at least 2 of the 8 positions. What is the maximum number of plates that can be issued?

Last edited by anna_gg (2016-01-12 08:29:24)

bobbym · 2016-01-12 08:10:03

Hi;

Can you please give the answer to the ice cream problem?

Math Is Fun Forum

#1 2016-01-04 01:45:15

Ice cream toppings

#2 2016-01-04 04:33:55

Re: Ice cream toppings

#3 2016-01-04 04:40:21

Re: Ice cream toppings

#4 2016-01-04 08:47:17

Re: Ice cream toppings

#5 2016-01-04 09:08:11

Re: Ice cream toppings

#6 2016-01-04 09:09:17

Re: Ice cream toppings

#7 2016-01-04 12:16:15

Re: Ice cream toppings

#8 2016-01-04 13:13:33

Re: Ice cream toppings

#9 2016-01-04 13:26:36

Re: Ice cream toppings

#10 2016-01-04 13:31:50

Re: Ice cream toppings

#11 2016-01-04 15:12:00

Re: Ice cream toppings

#12 2016-01-04 20:24:23

Re: Ice cream toppings

#13 2016-01-06 03:49:42

Re: Ice cream toppings

#14 2016-01-06 04:19:47

Re: Ice cream toppings

#15 2016-01-06 05:08:45

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#16 2016-01-06 06:51:39

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#17 2016-01-06 14:52:47

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#18 2016-01-06 21:22:35

Re: Ice cream toppings

#19 2016-01-06 21:34:09

Re: Ice cream toppings

#20 2016-01-07 22:27:25

Re: Ice cream toppings

#21 2016-01-08 00:29:55

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#22 2016-01-08 08:27:22

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#23 2016-01-08 16:20:33

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#24 2016-01-12 08:05:40

Re: Ice cream toppings

#25 2016-01-12 08:10:03

Re: Ice cream toppings

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