The classical football pool problem. The earliest and most natural problem, called the footballpoolproblem, is to try to construct a system for m matches which guarantees you at least the second prize. More generally, you wish to construct a system guaranteeing you at least the (r + l)st prize. Assuming that you already know beforehand (or think that you know) the outcome in some m - n matches reduces the problem to finding a similar system for n matches. Mathematically, we wish to find the smallest subset S of Z3ns uch that for every x E Z3nt here exists a word s E S such that d(x, s) < r, that is, the covering radius of S is at most r. This kind of covering radius problem has been widely studied in information theory [7, 8, 12, 31]. For r= 0 the solution is trivial: we simply take S = Z3n. For radius r = 1 the problem is already open in general. Example. Consider the case n = 4. It can be verified that each of the 81 points of Z3 iS within Hamming distance one from at least one of the nine words 0000, 0112, 0221, 1022, 1101, 1210, 2011, 2120, 2202. Since each word in Z3n has distance at most 1 to exactly 2n + 1 words in Z3n we know that when r = 1 we need to have at least 3n/(2n + 1) words in our system

SELECT * FROM user WHERE user_id>1;