シングマスター予想
120 = ( 120 1 ) = ( 120 119 ) = ( 16 2 ) = ( 16 14 ) = ( 10 3 ) = ( 10 7 ) {\displaystyle 120={120 \choose 1}={120 \choose 119}={16 \choose 2}={16 \choose 14}={10 \choose 3}={10 \choose 7}} 210 = ( 210 1 ) = ( 210 209 ) = ( 21 2 ) = ( 21 19 ) = ( 10 4 ) = ( 10 6 ) {\displaystyle 210={210 \choose 1}={210 \choose 209}={21 \choose 2}={21 \choose 19}={10 \choose 4}={10 \choose 6}} 1540 = ( 1540 1 ) = ( 1540 1539 ) = ( 56 2 ) = ( 56 54 ) = ( 22 3 ) = ( 22 19 ) {\displaystyle 1540={1540 \choose 1}={1540 \choose 1539}={56 \choose 2}={56 \choose 54}={22 \choose 3}={22 \choose 19}} 7140 = ( 7140 1 ) = ( 7140 7139 ) = ( 120 2 ) = ( 120 118 ) = ( 36 3 ) = ( 36 33 ) {\displaystyle 7140={7140 \choose 1}={7140 \choose 7139}={120 \choose 2}={120 \choose 118}={36 \choose 3}={36 \choose 33}} 11628 = ( 11628 1 ) = ( 11628 11627 ) = ( 153 2 ) = ( 153 151 ) = ( 19 5 ) = ( 19 14 ) {\displaystyle 11628={11628 \choose 1}={11628 \choose 11627}={153 \choose 2}={153 \choose 151}={19 \choose 5}={19 \choose 14}} 24310 = ( 24310 1 ) = ( 24310 24309 ) = ( 221 2 ) = ( 221 219 ) = ( 17 8 ) = ( 17 9 ) {\displaystyle 24310={24310 \choose 1}={24310 \choose 24309}={221 \choose 2}={221 \choose 219}={17 \choose 8}={17 \choose 9}}