a new Monty Hall riddle

The Riddler was sort of feeling the rising boredom of being under lockdown when proposing the following variant to the Monty Hall puzzle:

There are zero to three goats, with a probability ¼ each, and they are allocated to different doors uniformly among the three doors of the show. After the player chooses a door, Monty opens another door hidding a goat or signals this is impossible. Given that he did open a door, what is the probability that the player’s door does not hide a goat?

Indeed, a straightforward conditional probability computation considering all eight possible cases with the four cases corresponding to Monty opening a door leads to a probability of ³/₈ for the player’s door. As confirmed by the following R code:

s=sample
m=c(0,0)
for(t in 1:1e6)m=m+(range(s(1:3,s(1:3,1)))>1)

in the street for a year

Just like about every year, I sent two of my pictures to the photography competition of Paris Dauphine, with not much consideration for the theme “green the future”, and was hence quite surprised to get selected this time! (Almost as much surprised as last year when an almost perfect copy of my picture of the Alcazar Baths of Lady María de Padilla got selected!) As I could travel back from Oxford to attend the opening ceremony, I went there last night, wondering at which of my pictures had been selected (Lac Pavin, Auvergne versus the Quinrang, Skye)…

And so this picture will remain exposed in the street, boulevard Lannes, for the incoming year, meaning I will cross it each time I bike to the university! The 22 other pictures were more in tune with the theme of a green future, like the winning one of a fast moving métro carriage at the station Chemin Vert. Or this simple blade of grass growing from ashes…

 
And thus the winner is…

paradise island

As should be obvious from the pictures posted here in the past days, I have been away on vacations on the Scottish island of Skye, part of the Inner Hebrides. This is a place that had stood very high in my dream vacation places, mostly because of the mountain range that stands at the bottom of the island, called the Cuillins. There are 13 Munroes (tops above 3,000 feet) in that range and its entire traverse takes a very long day, including several belays. As I was there for a family vacation, we [alas!] only went up the easiest group, made of Sgùrr nan Gillean, Am Basteir, and Bruach na Frìthe, and did not climb Sgùrr nan Gillean. This was a fairly easy hike with a 900m differential, the only difficulty being in route finding. Which was made harder than needed by me first confusing a group of three hills with these Cuillins for the first third of the hike! And relating to instructions in our guidebook that covered the opposite side of the mountains. It was however a most pleasant walk, quite dry by Scottish standards (where it is often hard to separate water and soil) and with sun part of the way (it actually did not start to rain until the final half-hour). And not too many people on the path.
The other days saw easier walks at lower elevations, from a grassy and pleasant route to the top of MacLeod’s North Table [with terrific views of Western Skye and the Outer Hebrides], to a tour of the Gresornish peninsula under a pouring rain but with an amazing light (and an exciting crossing of a definitely web bog where even sheep did not do]. Overall, this was a great week in a secluded location, keeping mostly away from the few tourist traps [except for a trip to the Isle of Skye Brewery and to the compulsory Neist Point lighthouse] and I hope I can get back there one day. Although other Northern paradise islands like Mull, Harris, and the Faeroe are also beguiling..!
An unsolved puzzle about this visit to Skye is that, while there are sheep all over the island, which makes spotting any form of wildlife but midges impossible!, lamb meat is curiously absent from restaurant menus [except from the offal parts used in haggis]. The few persons we asked seemed perplexed by our question and had no convincing explanation to this absence!