Please help a struggling student with data set-up for lmer crossed random effects

Hi all,
I am just starting my first models in R and am having trouble with some of
the basics.

The main things at the moment are about setting up my data correctly.  I
have a repeated measures design-all participants complete 4 experimental
conditions. I want to fit a linear mixed effects model with crossed random
effects for subject and item. I have 4 conditions, 6 items per condition.
Because each condition uses different items, there are 24 total items. Each
group of 6 items only occurs in 1 condition, and it occurs in the same
condition for all participants. I am interested in including item as a
random effect in my model. My question is about labelling the items
correctly-should I label them 1-24, or 1-6 for each condition? I'm afraid if
I label 1-6 for each condition it will think item 1 was the same item and
was repeated in each of the four conditions. But if I label it 1-24 it will
look as though 18 of the items are missing in each condition as 6 can only
occur in any one condition.

subject item            condition
1               1               1
1               2               1
1               3               1
1               4               1
1               5               1
1               6               1
1               1               2
1               2               2
1               3               2
1               4               2
1               5               2
1               6               2
1               1               3
1               2               3
1               3               3
1               4               3
1               5               3
1               6               3
1               1               4
1               2               4
1               3               4
1               4               4
1               5               4
1               6               4

or like this:

subject item            condition
1               1               1
1               2               1
1               3               1
1               4               1
1               5               1
1               6               1
1               7               2
1               8               2
1               9               2
1               10              2
1               11              2
1               12              2
1               13              3
1               14              3
1               15              3
1               16              3
1               17              3
1               18              3
1               19              4
1               20              4
1               21              4
1               22              4
1               23              4
1               24              4

Sorry for the basic question, but I can't seem to figure this out!



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