# Two Sets: Solution for \( [1 \, .. n] \) When \( n \equiv 0 \pmod{4} \), solve as discussed previously with \( k = 1 \) and \( m = n \). When \( n \equiv 3 \pmod{4} \), * put \( 1 \) and \( 2 \) in the first result set, * put \( 3 \) in the second result set, and * then solve for \( [4 \, .. n] \) as discussed previously with \( k = 4 \) and \( m = n - 3 \). ## Illustration for \( n \equiv 3 \pmod{4} \) ``` .--------------------------. .---. | .------------------. | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 | | | | | | `---' | `-----------' ```