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One route was Tallinn-München-Sofia, the other one Tallinn-Kiev-Sofia. But then you had to calculate the distance from Kiev to Münich. When I came up with the solution, I didn't have enough time to carry it out.
 
If you connect Sofia and Tallin with one line and draw another line from Kiev to München, the two lines will cross at an angle, which will have a sine.

The sine of the cross.

If it is a regular cross, the sine of the cross equals 1.
 
I'm reading this paperless ticket stuff before tonight & it actually says "on the night of the event you will need to bring a printed copy of your confirmation email." So I'll need to bring a fucking piece of paper to prove I've bought a paperless ticket?! What. The. Fuck.
 
I reckon a lot of the venues aren't set up for fully paperless, not enough card scanners maybe. I don't know of anyone having ID checked as yet, and Ticketmaster was certainly sending tickets out for seating.
 
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