If you are willing to donate sufficient funds to pay all the extra costs of extending each Olympics by a full week, perhaps the IOC and all the LOCs would be willing to give your idea some consideration

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Good point about the extra cost that would be incurred by extending the length of the Olympics. I hadn't thought about that.
Although, there are ways that money could be saved in other areas that would enable this to happen. Such as granting the Olympics to cities that have a lot of the facilities already in place. But, that is another discussion altogether.
I would note that it is not unusual for the "opening ceremony" at figure skating events to take place after competition already has started.
Examples:
At 2017 Rostelecom, the Men's SP and the SD took place before the Opening on Ice.
At 2017 Skate Canada International, the Ladies SP and the SD took place before the Opening Ceremony.
If you have posted rants about figure skating schedules, I have missed them.
I have noticed that some figure skating competitions have Opening Ceremonies that are held after some of the SP's have been contested. But, to be honest, I haven't actually seen many Opening Ceremonies at figure skating competitions, so I don't know how common this practice is.
It is very rare that I even know that there is an Opening Ceremony at a figure skating competition, because they are normally not broadcast. I am one of those people that find the coloured Time Schedules very confusing. So, I just go by the timetable at the bottom of the Entries / Results Page. And they do not list Opening Ceremonies or Galas.
And now that Eurosport Player shoves the World Feed coverage of each segment into streams willy-nilly rather than having a dedicated stream for the World Feed coverage like they used to, there is less chance of catching them.
So, whenever I come across one, I don't complain in public because I am just grateful that I can watch it. But, I do have a wee grumble to myself.
Although, whenever there are snooker tournaments in China, they always have an Opening Ceremony in between the afternoon session and the evening session on the first day. And I normally do have a grumble to myself about the positioning of it.
Anyway, in the case of the 2018 Games, your original complaint that Eurosport cannot count (or that it does not realize competition starts a day before the Opening Ceremony) seems an odd way to express your real gripe -- which is with the IOC's scheduling.
Taking it out on Eurosport does not make sense to me.
Well, the way I look at it is that by having the graphic saying that today is 100 days to go, Eurosport are condoning the attitude that the things being held before the Opening Ceremony don't matter.
And as a ski jumping fan, I find it very disturbing that the channel for which ski jumping has been an integral part of the scheduling for over 20 years is condoning the view that the first day of the sport's Olympic schedule is not important.
So, that is why I am taking it out on Eurosport.
ETA:
I'm sure we all remember that the inaugural edition of the figure skating team event started the day before the Opening Ceremony in Sochi.
As a fan of the team event, I'm glad that the extra day of competition before the Opening Ceremony was allowed.
Otherwise, perhaps the IOC never would have approved the addition of the team event in the first place.
Don't start me on the Olympic Team Event. I didn't agree with it being added to the roster, because all it is doing is giving the skaters added pressure and extra opportunities to get injured before the most prestigious competition they can compete in.
I still feel that there are better ways that the time freed by the removal of the Compulsory Dance could have been used.
So, you are not going to coax me into saying that it starting before the Opening Ceremony is a good thing.
But, well done for trying.
CaroLiza_fan