The seventh grade class at a certain middle school decided to have an ice cream party to celebrate their outstanding grades. They decided to make ice cream cones. But they were all very independent thinkers, and they each wanted to have a different cone. Unfortunately the school was only willing to provide them with two ice cream flavors, vanilla and chocolate. They knew that if they used only single scoop cones, they could make only two different cones.

 

 

 

They figured out that if they used double scoop cones they could make four different cones.

 

 

 

There are 256 students in this outstanding class. How many scoops of ice cream would have to be used in each cone in order to make a different cone for each person.

Well I got 16

 

 

 

 

 

http://euclid.colorado.edu/~almann/math ... eamPOW.pdf

 

 

 

Check that out :o

Logical guess would be 16...

Thanks...Someone told me 8...

Oi, I was just about to ask if this was homework, to make sure I wouldn't be breaking the rules :x

Its not hw its extra credit...

if i did this right is very simple.

 

 

 

1=2

 

2=4

 

3=6

 

there for the equation is 2n

 

so 2n=x

 

2(256)=x

 

512=x

 

 

 

so 512 scoops for them to each have a different one?

nope, 2 scoops for 4 people

 

 

 

4 for 16

 

8 for 32

 

10 for 100

 

12 for 144

 

16 for 256..

 

 

 

Getting the pattern?

I dont think thats right...my teacher wouldnt do it that easily...I went:

 

 

 

2^1=2

 

.

 

.

 

.

 

.

 

.

 

2^8=256

Ahh i dont know what to do :cry:

oh well, i guess i kind of did it wrong, i tried to write it down, but word problems confuse me.i was comparing number of scoops to combinations. so i dont know what i did wrong.

'tis a pattten, you multiply the number to it self to find the amount of combinations....

Heh,

 

 

 

Square the number to find out the possible number of combinations.

 

 

 

In this case, since you have 256 students..

 

 

 

x^2 = 256

 

 

 

x = 16

 

 

 

:wink:

It's 8.

 

 

 

Since it has to be either one or the other you go go 2^n.

 

 

 

That is assuming all the students get the same number of scoops and that AB vs BA are not classified as the same type of ice cream. Neither of these points should be valid but occasionally teachers will try and throw them in.

 

 

 

2^1=2

 

A

 

B

 

 

 

2^2=4

 

AA

 

AB

 

BA

 

BB

 

 

 

2^3=8

 

AAA

 

AAB

 

ABA

 

ABB

 

BAA

 

BAB

 

BBA

 

BBB

 

 

 

Think of it this way.

 

For scoop 1 there is two possible types.

 

For scoop 2 there is two possible types

 

For them together you would go 2x2.

 

For scoop 3 there is two possible types.

 

So 2x2x2...

 

 

 

For instance with four scoops you can make all the types of three scoops and then add either an A or B to the beginning. Thus you multiply the amount in scoop 3 by two.

....................what grade are you in

 

nice job thaulsis

The problem here is that it's unknown whether or not sequence matters. Would ABB be considered the same as BAB and BBA?

I'm pretty sure that sequence matters, in this case, since they said that if there were two scoops there would be 4 possibilities.

 

 

 

Thaulsis is correct. There are a few classic errors to be made here, and the reason so many people are getting wrong answers, is that the initial pattern is "2, 4, ...". With only two data points, people will tend to go for the simplest possible solution, which is a straight line pattern, not an exponential one, which will lead you to the answer of 128... However, as Thaulsis explained, you have to think about how many additional possibilities are created by each additional scoop you add, which is to multiply the possibilities from (x-1) scoops by 2, to find out how many possibilities x scoops will give you. so you multiply 2 by itself x times. 2^x = 256. log base2 (256) = x =8... that is, 2 must be multiplied by itself 8 times to get 256.

 

 

 

Nvw, I don't understand what pattern you're going for.

wait wouldn't this be like a mathimatical combination? were the order doesn't matter? or is it a sort of permutation. anyways i know it's either 8 or 16