解:?$ (1)P=\frac {826 - 628}{22}=9,$?
因?yàn)?$9$?為整數(shù),
所以?$826$?為?$“$?有趣數(shù)?$”;$?
?$P=\frac {326 - 623}{22}=-13.5,$?
因?yàn)?$-13.5$?不是整數(shù),
所以?$326$?不是?$“$?有趣數(shù)?$”;$?
?$ (2)$?因?yàn)?$f = 100x + 42,$??$s = 120 + y(1\leqslant x\leqslant 9,$?
?$1\leqslant y\leqslant 9,$?且?$x,$??$y$?均為整數(shù)?$),$??$f$?和?$s $?的?$“$?有趣值?$”$?
分別記為?$P_{1}$?和?$P_{2},$?
所以?$P_{1}=\frac {100x + 42-(240 + x)}{22}=\frac {99x - 198}{22}=\frac {9(x - 2)}{2},$?
?$P_{2}=\frac {120 + y-(100y + 21)}{22}=\frac {99 - 99y}{22}=\frac {9(1 - y)}{2}。$?
因?yàn)?$P_{1}-2P_{2} = 36,$?
所以?$\frac {9(x - 2)}{2}-2×\frac {9(1 - y)}{2}=36,$?
整理可得?$x + 2y = 12。$?
因?yàn)?$1\leqslant x\leqslant 9,$??$1\leqslant y\leqslant 9,$?且?$x,$??$y$?均為整數(shù),
所以?$\begin {cases}x = 2 \\y = 5 \end {cases},$??$\begin {cases}x = 4 \\y = 4 \end {cases},$??$\begin {cases}x = 6 \\y = 3 \end {cases},$??$\begin {cases}x = 8\\y = 2 \end {cases}。$?
?$ $?將?$\begin {cases}x = 2\\y = 5 \end {cases}$?代入,可得
?$P_{1}=\frac {9×(2 - 2)}{2}=0,$?
?$P_{2}=\frac {9×(1 - 5)}{2}=-18,$?符合題意,
所以?$\begin {cases}f = 242\\s = 125 \end {cases};$?
將?$\begin {cases}x = 4\\y = 4 \end {cases}$?代入,可得
?$P_{1}=\frac {9×(4 - 2)}{2}=9,$?
?$P_{2}=\frac {9×(1 - 4)}{2}=-13.5,$??$-13.5$?不是整數(shù),不符
合題意;
將?$\begin {cases}x = 6\\y = 3 \end {cases}$?代入,可得
?$P_{1}=\frac {9×(6 - 2)}{2}=18,$?
?$P_{2}=\frac {9×(1 - 3)}{2}=-9,$?符合題意,
所以?$\begin {cases}f = 642\\s = 123 \end {cases};$?
將?$\begin {cases}x = 8\\y = 2 \end {cases}$?代入,可得
?$P_{1}=\frac {9×(8 - 2)}{2}=27,$?
?$P_{2}=\frac {9×(1 - 2)}{2}=-4.5,$??$-4.5$?不是整數(shù),不符合
題意。
所以滿足條件的三位數(shù)?$f$?和?$s $?分別為?$\begin {cases}f = 242\\s = 125 \end {cases}$?和
?$\begin {cases}f = 642\\s = 123 \end {cases}。$?