Nail-biting Eurovision Scoring 2016

Last night's Eurovision Song Contest Final saw an epic paradigm shift in the format of the 61 year-old competition. In the good-old days, those countries participating had 58 points to award the other competitors. They awarded 12 points to their favourite, 10 for their runner up, and 8,7,6,5,4,3,2, and 1 points to those songs they deemed the third to tenth best.

Eminent Ukrainian musicologists deliver their jury's considered verdict.

In recent years, various tweaks had dulled the excitement of the system. The most considerable had been the number of countries awarding points. All those countries knocked out at the semi-final stage are also allowed to join in. It is no surprise that the more points awarded, the greater the potential winning margin and so the greater the possibility that the last few juries will be irrelevant; it being mathematically impossible for a country whose lead is approximately a country mile to be overhauled.

Last year they jiggled the order of the juries' announcements to engineer a grandstand finish. It worked. Sort of. But they weren't satisfied.

This year, however, they tore up the rule book and made a scoring change that ripped through the beating heart of Eurovision Parties up and down the continent; particularly those including indolent guests who had not properly swotted up on the new system. After the juries' results had been announced, Australia - that newest of European countries - had a considerable lead of 109 points.

Australia tops the table after the jury votes

With all 2436 jury points cast this, in previous years, would have proved insurmountable.

In 2016, however, we were only half-way there; another 2436 points were to be awarded by the proletariat of the Eurovision community. In theory, an entrant could be awarded a further 492 points (douze from each of the countries they weren't representing) so that Germany, languishing on 1 point, might finish ahead of Australia. An interesting (but different) question might be whether, at this stage, the remaining points could be awarded in such a way that Germany finish ahead of everybody. I won't tackle that because it's a Sunday.

The points awarded from the public vote were summed for each country and announced in reverse. The game, therefore, was a bit like chicken; who could be left until last and benefit from the highest quantity of points? The guests at my own Eurovision party (a few of them maths teachers) became animated when they realised the consequence of the system, particularly when the UK's score was announced second.

Nigel Farage and Boris Johnson could prove the real winners here.

The UK's song, which the juries had not considered totally useless, was awarded 8 out of Europe's 2436 points. Four of these came from Australia (cheers), three from Ireland (T'anks), and one from Malta (have another cross). This confirms what we all suspected the rest of Europe think of us. In case you're planning your summer holidays, the following countries' populations ranked the UK song in last place: Belarus, Croatia, Hungary, Italy, Russia, and Serbia.

Anyway, I digress. Points were awarded in increasingly large quantities in quick succession for the least successful sixteen teams. Without a calculator to hand, it would have required some seriously sober summing to conclude that only 561 points had been awarded at this stage:

This meant the last ten teams would share 1875 points between them leaving scope for some dramatic scoreboard rearrangement.

Six more countries were added with points ranging from 96 for Lithuania to 180 for Bulgaria.

By this stage, with four countries remaining, I defy anyone who had been watching live to have made the following deduction: There were 1097 points left to award, the minimum quantity each being 180 and the maximum being 492. This means that Poland could now no longer win because Australia would finish on at least 500 and Poland would finish on at most 499. This is very pleasingly close.

At this stage Graham Norton said, "I think Australia have to win now". Not even the BBC knew what was going on.

Then. A shock. The next team to be awarded points - 191 of them - was Australia, giving them 511 in total. That left a huge 906 points left to be divided three ways with Ukraine needing 301 (one fewer than dividing these points equally) to win. The Ukraine would almost certainly win if they weren't read out next. But nobody knew that. Russia could still win at this stage.

Tragedy: She cheers because she hasn't done the maths.

Then Poland picked up 222 points leaving 684 to be awarded.

So Australia is on 511 points. Could they still win?

No. Definitively. No.

Either Ukraine scores 301 or more to beat them or scores 300 or less. This would mean Russia would score 384 or more, giving them a score of at least 514.

Ukraine versus Russia. Sound familiar?

The permutations are remarkably subtle and difficult to consider in real time. Remember, that the audience have lost track of how many points have been awarded. A Russian victory from here is a real mathematical possibility but would have been viewed as absolutely extraordinary.

In the end, Ukraine were awarded 323 which left Russia with 361. So our evenings concluded with another rendition of the uplifting Ukrainian song about ethnic cleansing in the Crimea.

Hurrah for Eurovision. Roll on a repeat of this genius numerical jeopardy in 2017.