Playing with memory homework

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algorithm

Playing with memory

Sindhu and Alistair play a memory game involving of a sequence of random
numbers between 1 and 10, inclusive, that is called out one at a time.

Each player can remember up to 5 previous numbers. When the called
number is in a player's memory, that player is awarded a point. If it's not,
the player adds the called number to his memory, removing another number
if his memory is full.

Both players start with empty memories. Both players always add new
missed numbers to their memory but use a different strategy in deciding
which number to remove:

Sindhu's strategy is to remove the number that hasn't been called in the
longest time.

Alistair's strategy is to remove the number that's been in the memory the
longest time.

Example game:

Turn Callednumber Sindhu's memory Sindhu's score Alistair's memory Alistair's score
1	1	  1	           0	         1	            0
2	2	  1,2	           0	         1,2	            0
3 	4	  1,2,4	           0	         1,2,4	            0 
4	6	  1,2,4,6	   0	         1,2,4,6	    0
5 	1	  1,2,4,6	   1	         1,2,4,6	    1
6	8	  1,2,4,6,8	   1	         1,2,4,6,8	    1
7	10	  1,4,6,8,10	   1	         2,4,6,8,10	    1
8	2	  1,2,6,8,10	   1	         2,4,6,8,10	    2
9	4	  1,2,4,8,10	   1	         2,4,6,8,10	    2
10	1	  1,2,4,8,10	   2	         1,4,6,8,10	    3
<blockquote class="FQ"><div class="FQA">Quote:</div>

Denoting Sindhu's score by S and Alistair's score by A.

The game is for a total of 20 called numbers, with the property that all
numbers would be called equal number of times (2 times each across 20
call-outs).

Given a set of 20 called numbers in a sequence, identify the winner of this game the earliest in the sequence.