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Chandler the Octopus is at a tentacle party! At this party, there is

1

creature with

2

tentacles,

2

creatures with

3

tentacles,

3

creatures with

4

tentacles, all the way up to

14

creatures with

15

tentacles. Each tentacle is distinguishable from all other tentacles. For some

2\le m < n \le 15

, a creature with m tentacles “meets” a creature with n tentacles; “meeting” another creature consists of shaking exactly 1 tentacle with each other. Find the number of ways there are to pick distinct

m < n

between

2

and

15

, inclusive, and then to pick a creature with

m

tentacles to “meet” a selected creature with

n

tentacles.
Proposed by Armaan Tipirneni, Richard Chen, and Denise the Octopus

Problem Statement