Browse problems

Place 33 distinct points with integer coordinates in \{0, \dots, 10000\}^2 , no three on a line, such that no 7 of them are in convex position (the vertices…

Status: solved (see Known). Kept as a template for matrix certificates. Find a 668 \times 668 matrix H with entries \pm 1 whose rows are pairwise orthogonal:…

Find a permutation c_0, \dots, c_{32} of \{0, \dots, 32\} (a mark in row r , column c_r ) such that all displacement vectors between marks are distinct: for…

Find 29 integers 0 = m_1 < m_2 < \dots < m_{29} \le 622 whose \binom{29}{2} = 406 pairwise differences m_j - m_i are all distinct (a Golomb ruler: no distance…

Find at most 72 words of length 6 over \{0, 1, 2\} such that each of the 3^6 = 729 words is within Hamming distance 1 of a chosen word (differs from it in at…

Colour each edge of the complete graph on the 43 vertices \{0, \dots, 42\} with one of two colours so that no 5 vertices have all \binom{5}{2} = 10 edges…

Place 2N = 142 points on the 71 \times 71 grid \{0, \dots, 70\}^2 so that no three of them lie on a common line, in any direction. Submit the points as [i, j]…

Colour the integers 1, \dots, 3704 with two colours so that no 7-term arithmetic progression a,\ a+s,\ a+2s,\ \dots,\ a+6s \qquad (s \ge 1) is monochromatic.…

Find three 10 \times 10 Latin squares S_1, S_2, S_3 on the symbols \{0, \dots, 9\} (each symbol once in every row and every column) that are pairwise…

Find 157 lines on the points \{0, \dots, 156\} , each a set of 13 points, such that any two lines meet in exactly one point, every point lies on exactly 13…