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Which Norwegian aircraft shared its type with the Germans?
Short answer
The Heinkel He 115, a German-built floatplane: the Royal Norwegian Navy Air Service (RNoNAS) had six He 115N in service when hostilities broke out, bought before the war. The Luftwaffe mainly used its own for laying mines, normally at night.

Six German floatplanes with Norwegian markings
Faced with rising tensions in Europe, the Norwegian Ministry of Defence ordered six He 115N for the Royal Norwegian Navy Air Service (RNoNAS), and the aircraft were delivered between 14 July and 13 November 1939. When hostilities broke out, the RNoNAS had six He 115N in service (F.50, F.52, F.54, F.56, F.58 and F.60), distributed along the coast from the naval air stations of Sola and Flatøy in the south to Skattøra, outside Tromsø, in the north. All of them were listed as operational.
Captures in both directions
At the start of the German invasion, the aircraft at the Hafrsfjord seaplane base, near Stavanger (F.60), was captured by the Germans, while an improvised Norwegian militia rifle unit seized two Luftwaffe He 115s at Ørnes, which received the codes F.62 and F.64 in Norwegian service. Seven Norwegian He 115s, five of them He 115N, were used against German or German-controlled ships.
The same type on both sides
The main mission of the Luftwaffe's He 115s was minelaying, usually at night to reduce the chance of being intercepted. Among the Norwegian aircraft that reached Britain were four German-built Heinkel He 115 floatplanes, and a fifth escaped to Finland.
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