Question

Study the pattern:
$1\ast 8+1=9$
$12\ast 8+2=98$
$123\ast 8+3=987$
$1234\ast 8+4=9876$
$12345\ast 8+5=98765$
Write the next two steps, can you say how the pattern works?
(Hint: $12345=11111+1111+111+11+1$ ).

Answer 1

$123456\ast 8+6=987648+6=987654$
$1234567\ast 8+7=9876536+7=9876543$
Yes, the pattern works.
As $123456=111111+11111+1111+111+11+1$.
$123456\ast 8=(111111+11111+1111+111+11+1)\ast 8$
$=111111\ast 8+11111\ast 8+1111\ast 8+111\ast 8+11\ast 8+1\ast 8$
$=888888+88888+8888+888+88+8=987648$
$=123456\ast 8+6=987648+6=987654$