[maximin] geometric climbing

A puzzle from The Riddler this week returning to the ranking of climbing competitors in Tokyo. And asking for the maximin score, that is, the worst possible absolute score guaranteeing victory. In the case of eight competitors, a random search for a maximin over 10⁶ draws leads to a value of 48=1x7x8, for a distribution of ranks as follows

[1,]    1    8    8
[2,]    2    6    4
[3,]    3    4    5
[4,]    4    2    6
[5,]    5    5    2
[6,]    6    3    3
[7,]    7    7    1
[8,]    8    1    7

while over seven competitors (the case with men this year, since one of the brothers Mawem got hurt during the qualification), the value is 35=1x5x7, for a distribution of ranks as follows

[1,]    1    7    5
[2,]    2    3    6
[3,]    3    4    3
[4,]    4    5    2
[5,]    5    2    4
[6,]    6    1    7
[7,]    7    6    1

exhibiting a tie in the later case (and no first position for the winners!).

death of a marathoner

In connection with the 2021 Tokyo Olympics, I read a poignant story in the New York Times, relating the short life of marathoner Kōkichi Tsuburaya, who finished third in the 1964 Tokyo Olympics, in 2:16:22, being passed on the final lap by Basil Heatley from Britain. He felt like committing a “blunder” in front of his compatriots. And he invested so heavily in his training for the 1968 Mexico Olympics, with such poor training from his coaches that he kept facing injuries. And committed suicide a few months before the Olympics… In memoriam.

geometric climbing

On the qualifying round for the Tokyo Olympics, the French climber Mickaël Mawem ended up first, while his brother Bassa was the fastest on the speed climb (as a 2018 and 2019 World Champion) but ruptured a tendon while lead climbing and had to be flown back to Paris for a operation. The New York Times inappropriately and condescendingly qualified this first position as being “unexpected” when Mickaël is the 2019 European Champion in bouldering… The NYT is piling up in its belittling by stating that “Anouck Jaubert of France used a second-place finish in speed to squeak into the final¨… (The other French female climber did not make it, despite being one of the first women to reach the 9b level.)

I remain puzzled by the whole concept of mixing the three sports together. As well as by the scoring system, based on a geometric average of the three rankings, which means in particular that the eight finalists will suffer less than in the qualifying round from a poor performance in one of the three climbs (as Adam Ondra for the speed climb). In addition, there is an obscure advantage coming to Adam Ondra for Bassa Mawem cancelling his participation: according to the NYT, “Ondra will receive a bye and an automatic slot in the speed semifinals” meaning “that a likely eighth-place finish in speed — a ranking number that can be hard to overcome in the multiplication of the combined format — will now be no worse than fourth for Ondra”. (The sentence on the strong impact due to the geometric mean is incorrect in that it has less impact that the arithmetic!)

golden revenge

Sumo [France TV on Tokyo Olympics]