Gauss died in 1855 and so the riddle is asking to sum 1 to 1855. Upon summing these numbers you will get a seven digit number. In the story, the characters figure out that this seven digit number is a phone number and use it to get their next riddle. Around the time that they wrote the story, we had been discussing series and had talked about how to find the sum from 1 to any positive integer. I had told them about the (almost certainly apocryphal) story of how a 10-year old Gauss solved the problem of adding 1 to 100 quickly which they cleverly incorporated into their story.