There are 60 records given to you which correspond to a prisoner who is imprisoned for 60
days. He has 6 relatives one of whom visits him daily and the others visit him every i
th day from the day of his imprisonment (i=2,3,4,5,6 for these 5 relatives).
Every record is sealed with the day number on it which indicates the number of days he is jailed when the record is filed with the names of visitors on that particular day. You have to make a new record which should be filled with the following details:
visitor name - number of visits after 60 days
Assume that no other relatives visited him at all, names of these 6 relatives are different and you don't know their names. Find the minimum number of records that need to be checked to make the new record correctly. Find the number of ways you can choose the minimum number of records and you can still make the new record correctly.
Given that it's been settled that 3 are necessary and sufficient, the following program determines the 80 sets of 3 that will work.
OPEN "prisvis.txt" FOR OUTPUT AS #2
FOR a = 1 TO 58
FOR b = a + 1 TO 59
FOR c = b + 1 TO 60
FOR i = 1 TO 6
IF a MOD i = 0 THEN result(i) = 4: ELSE result(i) = 0
IF b MOD i = 0 THEN result(i) = result(i) OR 2
IF c MOD i = 0 THEN result(i) = result(i) OR 1
NEXT
good = 1
FOR i = 1 TO 5
IF result(i) = 0 THEN good = 0
FOR j = i + 1 TO 6
IF result(i) = result(j) THEN good = 0
NEXT
NEXT
IF result(6) = 0 THEN good = 0
IF good THEN
PRINT a; b; c; : ct = ct + 1
FOR i = 1 TO 6
PRINT LTRIM$(STR$(result(i)));
NEXT
PRINT
PRINT #2, a; b; c;
FOR i = 1 TO 6
PRINT #2, LTRIM$(STR$(result(i)));
NEXT
PRINT #2,
END IF
NEXT
NEXT
NEXT
PRINT ct
The table shows all the sets. After each set of three, there is a set of six digits, each digit representing one of the visitors. If the digit that represnts any given visitor is represented in binary, it tells, by its three binary digits, which of the three records will show his name.
For example, the first set in the right hand column is 15, 18, 52. The sequence of visitor digits is 736142, indicating visitor 1 will be on all three (7=111), visitor 2 will be on only the last two (3=011), visitor 3 will be on only the first two (6=110), visitor 4 will be on only the last record (1=001), visitor 5 on only the first record (4=100) and visitor 6 on only the middle record (2=010).
4 6 15 763412 15 18 52 736142
4 6 45 763412 15 18 56 736142
4 15 18 753421 15 20 42 735261
4 15 42 753421 15 20 54 735261
4 15 54 753421 15 28 42 735241
4 18 45 763412 15 28 54 735241
4 42 45 763412 15 32 42 735241
4 45 54 753421 15 32 54 735241
6 8 15 765214 15 40 42 735261
6 8 45 765214 15 40 54 735261
6 15 16 756124 15 42 44 736142
6 15 20 756134 15 42 52 736142
6 15 28 756124 15 42 56 736142
6 15 32 756124 15 44 54 735241
6 15 40 756134 15 52 54 735241
6 15 44 756124 15 54 56 736142
6 15 52 756124 16 18 45 763412
6 15 56 756124 16 42 45 763412
6 16 45 765214 16 45 54 753421
6 20 45 765234 18 20 45 765234
6 28 45 765214 18 28 45 765214
6 32 45 765214 18 32 45 765214
6 40 45 765234 18 40 45 765234
6 44 45 765214 18 44 45 765214
6 45 52 756124 18 45 52 756124
6 45 56 756124 18 45 56 756124
8 15 18 753421 20 42 45 763452
8 15 42 753421 20 45 54 753461
8 15 54 753421 28 42 45 763412
8 18 45 763412 28 45 54 753421
8 42 45 763412 32 42 45 763412
8 45 54 753421 32 45 54 753421
15 16 18 735241 40 42 45 763452
15 16 42 735241 40 45 54 753461
15 16 54 735241 42 44 45 765214
15 18 20 736152 42 45 52 756124
15 18 28 736142 42 45 56 756124
15 18 32 736142 44 45 54 753421
15 18 40 736152 45 52 54 735241
15 18 44 736142 45 54 56 736142
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Posted by Charlie
on 2009-01-22 03:38:04 |
computer calculation
