12345
Repeat a pattern of numbers to form a larger number. Can you find the sum of all the digits?
Age
14 to 16
Challenge level
The pattern 123451234512345... is continued to form a 2000 digit number.
What is the sum of all 2000 digits?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Answer: $6000$
$\underbrace{\overbrace{12345}^{15}\overbrace{12345}^{15}\overbrace{12345}^{15}\dots\overbrace{12345}^{15}}_\text{2000 digits}$
Total: $15\times(2000\div5) = 6000$
Alternatively, the mean of each group of five digits is $3$ and so the mean of the digits making up the number is $3$. Therefore the sum is $2000\times 3=6000$.
Note that this only works because the groups are in $5$s, and $5$ goes into $2000$ exactly