Mini Sudoku: see www.englishedmoscow.com
Top row: Frunzenskaya – Bolotnaya (over the canal) – Kievskaya
Bottom: Prechistenskaya (over the river, next to Christ the Saviour) - Luzhkov (the wedding bridge) – Tessinssky (on the Yauza)
Neither Konigsberg nor Moscow can be walked in a single tour, as in each case there are more than two places with 1, 3 or 5 routes. With an odd number of routes, you must start or finish there, so there can be no more than two places like this. In both cities, building or removing any bridge, anywhere allows the walk to be done. Try it!
The students are 16: 23x2 this year, 3x5 last year. I could be 40 (23x5 now, after 3x13); 56 (23x7, 5x11) or 88 (23x11, 3x29); but also 23 (now 13x23, earlier 2x11), 47 (13x47; 2x23), 59 (13x59, 2x29) or 83 (13x83, 2x41).