Invite All Your Friends! (example puzzle)

In the past few years, the Elfbook app has gone viral on the North Pole; most elves have created a profile and invited their friends to see their timelines. Now, Elfbook invitations are the easiest way to spread word about an event. To prevent these events from attracting too many elves and stirring trouble in the village, the number of invites for one event is limited to a maximum of 40 per elf.

Frodo and Holgar are now planning a Christmas party. “A small thing, nothing fancy”, is what they agree on. When it comes to choosing the invite settings on Elfbook, Frodo says: “I will invite all of my friends – that’s 21 invites. To mix it up a little I will also allow them to invite all of their friends!”

“Hold on,” cautions Holgar. “All of your friends have more friends than you. If you choose these invite settings, your house will explode with elves!”

“Ah, I don’t believe that”, replies Frodo and hits the “Send” button…

With Frodo’s chosen invite settings, which of the following statements regarding his event invitations on Elfbook is correct?


a) Exactly 40 invitations will be sent out in total.

b) Between 60 and 589 elves will receive an invitation.

c) There will be at least 780 elves invited.

d) In the worst case scenario, a total of 840 elves will be invited.

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