I ran a search out to a billion & found 109 examples. There were no cases of A, B and C distinct, and they pretty much all fell into a few simple patterns. Here's the list: 15=5+5+5 19=1+9+9 150=50+50+50 182=18+82+82 191=9+91+91 195=5+95+95 199=1+99+99 1500=500+500+500 1819=181+819+819 1950=50+950+950 1981=19+981+981 1991=9+991+991 1995=5+995+995 1999=1+999+999 15000=5000+5000+5000 18182=1818+8182+8182 19091=909+9091+9091 19500=500+9500+9500 19802=198+9802+9802 19901=99+9901+9901 19950=50+9950+9950 19981=19+9981+9981 19991=9+9991+9991 19995=5+9995+9995 19999=1+9999+9999 150000=50000+50000+50000 181819=18181+81819+81819 195000=5000+95000+95000 198020=1980+98020+98020 199010=990+99010+99010 199091=909+99091+99091 199500=500+99500+99500 199801=199+99801+99801 199901=99+99901+99901 199950=50+99950+99950 199981=19+99981+99981 199991=9+99991+99991 199995=5+99995+99995 199999=1+99999+99999 1500000=500000+500000+500000 1818182=181818+818182+818182 1909091=90909+909091+909091 1950000=50000+950000+950000 1980199=19801+980199+980199 1995000=5000+995000+995000 1998002=1998+998002+998002 1999001=999+999001+999001 1999010=990+999010+999010 1999091=909+999091+999091 1999500=500+999500+999500 1999801=199+999801+999801 1999901=99+999901+999901 1999950=50+999950+999950 1999981=19+999981+999981 1999991=9+999991+999991 1999995=5+999995+999995 1999999=1+999999+999999 15000000=5000000+5000000+5000000 18181819=1818181+8181819+8181819 19500000=500000+9500000+9500000 19801981=198019+9801981+9801981 19900991=99009+9900991+9900991 19909091=90909+9909091+9909091 19950000=50000+9950000+9950000 19980020=19980+9980020+9980020 19990010=9990+9990010+9990010 19995000=5000+9995000+9995000 19998001=1999+9998001+9998001 19999001=999+9999001+9999001 19999010=990+9999010+9999010 19999091=909+9999091+9999091 19999500=500+9999500+9999500 19999801=199+9999801+9999801 19999901=99+9999901+9999901 19999950=50+9999950+9999950 19999981=19+9999981+9999981 19999991=9+9999991+9999991 19999995=5+9999995+9999995 19999999=1+9999999+9999999 150000000=50000000+50000000+50000000 181818182=18181818+81818182+81818182 190909091=9090909+90909091+90909091 195000000=5000000+95000000+95000000 198019802=1980198+98019802+98019802 199009901=990099+99009901+99009901 199500000=500000+99500000+99500000 199800200=199800+99800200+99800200 199900100=99900+99900100+99900100 199900991=99009+99900991+99900991 199909091=90909+99909091+99909091 199950000=50000+99950000+99950000 199980002=19998+99980002+99980002 199990001=9999+99990001+99990001 199990010=9990+99990010+99990010 199995000=5000+99995000+99995000 199998001=1999+99998001+99998001 199999001=999+99999001+99999001 199999010=990+99999010+99999010 199999091=909+99999091+99999091 199999500=500+99999500+99999500 199999801=199+99999801+99999801 199999901=99+99999901+99999901 199999950=50+99999950+99999950 199999981=19+99999981+99999981 199999991=9+99999991+99999991 199999995=5+99999995+99999995 199999999=1+99999999+99999999 On Mon, Feb 24, 2020 at 3:58 AM Éric Angelini <bk263401@skynet.be> wrote:
Hello Math-Fun, do you know any other solutions? (especially where A, B and C are distinct)
1818 = A 8182 = B + 8182 = C ------ = 18182 = D
Best, É.
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