abcd+dcba=xx0xx
1000•a+100•b+10•c+d+1000•d+100•c+10•b+a=11011•x
1001•a+110•b+110•c+1001•d=11011•d /:11
91•a+91•d+10•b+10•c=1001•x
10(b+c)=91·(11•x-a-d)
=> b=c=0
11•x-a-d=0
11•x=a+d
x=1=> a+d=11
a=2; d=9; abcd=2009
a=3; c=8; abcd=3008
a=4; d=7; abcd=4007
a=5; d=6; abcd=5006
a=6; d=5; abcd=6005
a=7; d=4; abcd=7004
a=8; d=3; abcd=8003
a=9; d=2; abcd=9002
abcd∈{2009; 3008; 4007; 5006; 6005; 7004; 8003; 9002}
