Study the pattern :
1 8 + 1 = 9 1234 8 + 4 = 9876
12 8 + 2 = 98 12345 8 + 5 = 98765
123 8 + 3 = 987
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).
123456 8 + 6 = 987648 + 6 = 987654
1234567 8 + 7 = 9876536 + 7 = 9876543
Yes, the pattern works.
As 123456 = 111111 + 11111 + 1111 + 111 + 11 + 1,
123456 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) 8
= 111111 8 + 11111 8 + 1111 8 + 111 8 + 11 8 + 1 8
= 888888 + 88888 + 8888 + 888 + 88 + 8
= 987648
And,
123456 8 + 6 = 987648 + 6 = 987648