Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2023 IOQM/Problem 16

Revision as of 15:22, 1 May 2024 by L13832 (talk | contribs) (Created page with "==Problem== The sides of a convex hexagon <math>A_1A_2A_3A_4A_5A_6</math> are coloured red. Each of the diagonal of the hexagon is coloured red or blue. If N is the number of...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

The sides of a convex hexagon $A_1A_2A_3A_4A_5A_6$ are coloured red. Each of the diagonal of the hexagon is coloured red or blue. If N is the number of colourings suhch that every triangle $A_iA_jA_k$, where $1\ge i\ge j\ge k\ge 6$ has at least one red side, find the sum if the squares of digits of N.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_IOQM/Problem_16&oldid=218932"