Thread: Problem Solving

At the local grocery store, there is a very strict code that the shop assistants must adhere to. When a customer asks for a certain number of potatoes, he or she must first take potatoes from the crate containing bags of 3 potatoes only and then take potatoes from the crate containing bags of 5 potatoes only. The shop assistant cannot come back to the crate with bags of 3 potatoes. He/she can choose take to as many bags from either crate provided there is at least one taken from each sack.

One day, a customer visited the store and told the shop assistant that he would like X number of potatoes. The shop assistant figured out how he should give the customer the exact number of potatoes he had requested but he discovered there was only one way to do this.

What is X? Find all possible solutions.

i'm not sure i understand the problem...is that word for word from your text.
are they asking for a graph or a numarical sultion?

i'd like to help but i'm not sure what the questian is
dan

Hey Dan, I'm suffering from the same problem you are, I'm not exactly sure what the question is asking.

I believe X could be

3a+5b

where a and b can be any integers larger than 1

is this a suitable answer?

Can the clerk take potatoes out of the sacks? If not then what is he supposed to do for 2 potatoes.

Don't think he can take potatoes out of the sacks!!!

That's the point, he can't provide ANY number of potatoes, it just has to adhere to the rules.

It's a very confusing question.

Originally Posted by cliveanderson

Hey Dan, I'm suffering from the same problem you are, I'm not exactly sure what the question is asking.

I believe X could be

3^a +5

3+5^b

3^a+5^b

where a and b can be any integers larger than 1

is this a suitable answer?

How many ways can the clerk make 11 potatoes?
Is 11 of the form 3^a+5^b, a,b>0?

RonL

Consider any total T greater than 30. If it can be written:

T=3.n+5m

n,m>0, then it can be met subject to the constraints.

Also (if it can be met) either n>5, or m>3.

Suppose n>5, then:

T=3.(n-5)+5,(m+3),

and as (n-5)>0, and (m+3)>0, T can be met in at least two ways.

A similar argument applies if m>3.

So if X is a total that can be met in exactly one way X<=30

RonL

Hey CaptainBlack,

Thanks for your reply but could you clarify something for me?

If only n>5, then the total is not 30 or over?

I can see that your method of working this out works but could you explain it?

Thanks in advance, I appreciate your help!

Originally Posted by cliveanderson

Hey CaptainBlack,

Thanks for your reply but could you clarify something for me?

If only n>5, then the total is not 30 or over?

m must be at least >=1, to make up the difference, also maybe the
value of 30 can be trimmed a bit (I don't remember why I chose 30
in the end I started out with 23 for this value but revised it upwards
for reasons I don't recall now).

The main idea is that if the number of sacks of 3 is large enough
you can always replace 5 of them by 3 sacks of 5, and the same
sort of argument applies if the number of sacks of 5 is large enough.
Also if the total is can be made up and is sufficiently large either the
number of sacks of 3 or 5 will be large enough, so there will be multiple
ways of making a total given that it can be made.

RonL

Thanks to CaptainBlack's help, I was able to successfully solve the problem!!

n cannot be greater than 5, otherwise 15 of these potatoes can be replaced by the sacks with 5 potatoes

m cannot be greater than 3, vice versa with above

Thank you very much!

I don't really like this problem. Consider a customer buying 4 potatoes. It is perfectly legal to get 2 sacs of three and take 4 out of them. But it is also perfectly legal to get a sac of 3 and a sac of 5 and take 4 out of them. In this reason there is no actual value of x unless you put a restriction up...