Tuymaada Yakut Olympiad 2000, Problem 3
Source:
July 24, 2012
calculusintegrationcombinatorics
Problem Statement
Can the 'brick wall' (infinite in all directions) drawn at the picture be made of wires of length (each positive integral length occurs exactly once)? (Wires can be bent but should not overlap; size of a 'brick' is ).[asy]
unitsize(0.5 cm);for(int i = 1; i <= 9; ++i) {
draw((0,i)--(10,i));
}for(int i = 0; i <= 4; ++i) {
for(int j = 0; j <= 4; ++j) {
draw((2*i + 1,2*j)--(2*i + 1,2*j + 1));
}
}for(int i = 0; i <= 3; ++i) {
for(int j = 0; j <= 4; ++j) {
draw((2*i + 2,2*j + 1)--(2*i + 2,2*j + 2));
}
}
[/asy]