Four-digit 10261

Roman likes magic and math. Last time he conjured three- or four-digit numbers like this:
• created two new numbers from the given number by dividing it between digits in the place of hundreds and tens (e.g., from the number 581, he would get 5 and 81),
• added the new numbers and wrote down the result (in the example given, he would get 86),
• subtracted the smaller ones from the larger of the new numbers and wrote the result after the previous sum, thus conjuring the resulting number (in the example given, he would get 8676).

Which numbers could Roman conjure
a) 171,
b) 1513? Specify all options.

What is the largest number we can conjure in this way, and from which numbers can it arise? Identify all

Correct answer:

x1 =  114
x2 =  809
x3 =  908
x4 =  1401
x5 =  7477
x6 =  7774
x7 =  18810

Step-by-step explanation:

x1=114 p11=1 p21=14 s1=p11+p21=1+14=15 o=p11p21=114=13 c1=1513
x2=809 p12=8 p22=9 s2=p12+p22=8+9=17 o=p12p22=89=1 c2=171
x3=908 p13=9 p23=8 s3=p13+p23=9+8=17 o=p13p23=98=1 c3=171
x4=1401 p14=14 p24=1 s4=p14+p24=14+1=15 o=p14p24=141=13 c4=1513
x5=7477 p15=74 p25=77 s5=p15+p25=74+77=151 o=p15p25=7477=3 c5=1513
x6=7774 p16=77 p26=74 s6=p16+p26=77+74=151 o=p16p26=7774=3 c6=1513
x7=18810 c = { 8999, 9989 } p17=8999 p27=9989 s7=p17+p27=8999+9989=18988 o=p17p27=89999989=990

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