I participated in the contest. I solved that, because it was one of the easiest tasks.
The thing is that you wrote all these intermediate calculations, which are not allowed in the competitions.
We are only allowed to write the final result.
That task was particularly easy because the divisor has the same digits (2,2 and 2) . So, every multiple up to 9, is found instantly 222, 444, 666, 888, 1110, 1332, 1554, 1776, 1998. (at least for world cup level)
So, essentially it is just a dozen of easy subtractions, 3 or 4 digits at a time. Also, it is crucial to remember the zeros.
We had to do around 100 of these tasks in 10 minutes, so it was expected to find this remainder in 6 seconds (in perfect circumstances.)
But most calculators including me, took at least 20 sec, to find such a remainder (mod222) , because one has to be careful and accurate.
For example, if you found 33mod222 or 35mod222 instead of the correct 34mod222, then you get ZERO points (instead of 1 point.). These are the rules, and there is no lenience for getting close to the result. You either find the correct result or not. It is black or white.
Also, potential markings on the paper which indicate intermediate steps, result in instant disqualification. The reason being that it is mental math and not high school math.
We only write down the final result, for practical reasons, just to ensure simultaneous fairness among competitors, because time-wise it would take too long for the judges to make everyone recite the result individually.
In the contest , I think , I found around 20 of such mods. I recall that mod101, mod222 and mod444 were probably the only 3 digit mods that I picked. The others, were small easy ones like 7, 11, 14, 27, 33, 44 and so on, which are also very easy to divide in.
Out of these 100 mods , we could choose to do as many as we could in 10 minutes. And if one found 20, 30, or 40 correct, that was considered a very good result. I don’t think many people found more than 60 out of 100. I will ask Wenzel (who won these surprises), about how many did he found, but I think he was somewhere between 60 and 80 correct. (due to time limitation of 10 minutes).
Bjoern participated also, and maybe he can remember more details , methods or results about that task.
Nodas, Greek competitor
2nd place Calendar, MC World Cup 2018