## Problem 709 - Even Stevens

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Chappen
Posts: 2
Joined: Mon Apr 27, 2020 6:49 pm

### Problem 709 - Even Stevens

Hello everyone. I've had quite a hard time understanding the logic behind Problem 709 - Even Stevens. So let's just use the example they give in the problem to illustrate my issue:

After 4 days there are 5 possible packings and if the bags are numbered 1 (oldest), 2, 3, 4, they are:
1. Four empty bags,
2. 1 and 2 inside 3, 4 empty,
3. 1 and 3 inside 4, 2 empty,
4. 1 and 2 inside 4, 3 empty,
5. 2 and 3 inside 4, 1 empty.

How can this be? Isn't this inconsistent? If packaging 2 & 4 both use the same bags but leave diffrent bags empty then it follows that packaging 3 & 5 should be able to do the same, which results in 7 possible packings. Or 2 & 4 shouldn't be allowed swap empty bag and thus we reach 4 possible packings.

Please tell me if I'm wrong but I believe this problem has a false answer since I can come to the conclution that f(4) = 7 or 4 or 13 but not 5.
wrongrook
Posts: 470
Joined: Sat Oct 17, 2009 10:39 pm

### Re: Problem 709 - Even Stevens

Packaging 2 and 4 are built up in different ways.

2 comes from:
A) place bag 1 inside
B) place bag 2 inside
C) place 1 and 2 in bag 3
D) place bag 4 inside

4 comes from:
A) place bag 1 inside
B) place bag 2 inside
C) place bag 3 inside
D) place bag 1 and 2 in bag 4

In other words, you are right that you are not allowed to swap the empty bag.
Chappen
Posts: 2
Joined: Mon Apr 27, 2020 6:49 pm

### Re: Problem 709 - Even Stevens

wrongrook wrote: Mon Apr 27, 2020 8:11 pm Packaging 2 and 4 are built up in different ways.

2 comes from:
A) place bag 1 inside
B) place bag 2 inside
C) place 1 and 2 in bag 3
D) place bag 4 inside

4 comes from:
A) place bag 1 inside
B) place bag 2 inside
C) place bag 3 inside
D) place bag 1 and 2 in bag 4

In other words, you are right that you are not allowed to swap the empty bag.
I'm not quite sure I understand what you mean. Even so, how does taking this packaging differance into a account change anything? If i do what you did for the rest I get the following:

1. Four empty bags,
1 comes from:
A) Place all bags inside

2. 1 and 2 inside 3, 4 empty,
2 comes from:
A) place bag 1 inside
B) place bag 2 inside
C) place 1 and 2 in bag 3
D) place bag 4 inside

3. 1 and 3 inside 4, 2 empty,
3 then comes from:
A) place bag 1 inside
B) place bag 3 inside
C) place bag 1 and 3 in bag 4
D) place bag 2 inside

4. 1 and 2 inside 4, 3 empty,
4 comes from:
A) place bag 1 inside
B) place bag 2 inside
C) place bag 3 inside
D) place bag 1 and 2 in bag 4

5. 2 and 3 inside 4, 1 empty,
5 then comes from:
A) place bag 2 inside
B) place bag 3 inside
C) place bag 2 and 3 in bag 4
D) place bag 1 inside

6. 1 and 3 inside 2, 4 empty,
6 then comes from:
A) place bag 1 inside
B) place bag 3 inside
C) place bag 4 inside
D) place bag 1 and 3 in bag 2

7. 2 and 3 inside 1, 4 empty,
7 then comes from:
A) place bag 2 inside
B) place bag 3 inside
C) place bag 1 inside
D) place bag 2 and 3 in bag 1
wrongrook
Posts: 470
Joined: Sat Oct 17, 2009 10:39 pm

### Re: Problem 709 - Even Stevens

Each time you need to either place the new bag inside the cupboard empty, or place bags inside the new bag.

This means that your example 7 is invalid because in step D you cannot put bags into bag 1 (as it is not the new bag).