## Concatenation | 7-digit number abc = a || b || c

a,   b,   c   are in arithmetic progression

a   ||   b   ||   c   =   abc   is a 7-digit number

Find the largest 7-digit number obtained in this way.

K.D. BAJPAI

9500991   =   9   ||   500   ||   991   with common difference   491
9899100   =   98   ||   99   ||   100   with common difference   1

Paul:

the largest 8-digit number with 3 concatenations

9   ||   999   ||   1989   with common difference   990.

the largest 9-digit number with 3 concatenations

999   ||   998   ||   997   common diff of   1

the largest 10-digit number with 3 concatenations

9   ||   9999   ||   19989   common diff of   9990

math grad - Interest: Number theory
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### 5 Responses to Concatenation | 7-digit number abc = a || b || c

1. K.D. BAJPAI says:

9500991 : 9||500||991 with common difference 491.

2. K.D. BAJPAI says:

9899100 : 98||99||100 with common difference 1.

3. paul says:

Here is the largest 8 digit number with 3 concatenations

9 || 999 ||1989 with common difference 990.

Paul.

• paul says:

The 9 digit one seemed trivial with

999 || 998 || 997 common diff of 1

and the 10 digit one is

9 || 9999 || 19989 common diff of 9990

Paul.