The brainbuster

What is the next line in this sequence?

i i
ii i
i ii i i
i i i ii ii i
iii i ii ii i i
i iii i i ii ii ii i

Only complete entry forms will be considered.

The competition closed on Sunday 29th September 2013.

The entries

There was a good number of responses and nearly every entry was correct. We suspect that where the wrong answer was given, it was simply a matter of double checking to ensure you'd typed the answer correctly!

The solution

Here is the answer as given by our winner:

The correct answer is i i i iii ii i iii ii i i

Each line of the original sequence is obtained by counting the number of consecutive occurrence of each numeral, writing down the count in Roman numerals followed by the relevant numeral.

Thus for example the penultimate row is iii i ii ii i i. iii occurs once so we write down i iii. i occurs once so we write down i i. ii occurs twice so we write down ii ii. i occurs twice so we write down ii i. So the final line as given in the question is i iii i i ii ii ii i. Finally we have 1 lot of i, 1 lot of iii, 2 lots of i, 3 lots of ii, 1 lot of i, which gives us the solution above.

And the winner is...

The winner of ecm's brainbuster no. 35 is Dr Jeremy Wilson, an experienced Java developer who graduated from Imperial College.

Congratulations again to Jeremy, and watch out for ecm's next brainbuster !