[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!).

IFSC 2020, Briançon [jatp]

 

Adam Ondra completes a first 9c

In my office hangs this poster of Adam Ondra climbing at sunset an impressive overhang with a little Czech town at the foot of the cliff, already in the shade. Impressive because of the view and of the climb which at 7c is a whole grade (and then some) beyond my reach. But now Ondra has managed to climb the first 9c in the world, which is universes beyond the impressive and beyond the fathomable, with passages only manageable feet first. Which actually makes a lot of sense, the way he explains it. The route is currently called Project Hard and is located in Hanshelleren Cave, Flatanger, Norway.