This is about \$n\$ by \$n\$ binary matrices. Call a pair of rows unfriendly if the Hamming distance between the two rows is larger than the number ones they have in common positions. Let us call a matrix unfriendly if all pairs of rows are unfriendly. The identity matrix is, for example, unfrien...

The "schoolgirls problem" posed and answered by Kirkman in 1850 is: "Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast." Also in 1850, Sylvester asked whether it is possible for the gi...

Given the truth table of a non-trivial symmetric 2-input logic gate, output its name. The 6 possible input/output pairs are: 0001 -> AND 1110 -> NAND 0111 -> OR 1000 -> NOR 0110 -> XOR 1001 -> XNOR (where the 4 symbols represent the outputs of the gate for inputs 00,01,10,11 respectively). Inpu...