# Welcome To Math-Update´s Advent Calendar 2000 + 2^2^2 ….. Day #1: Best X-MATHS Gift! – Yorgey´s Factorization Diagrams

Our Advent Calendar intends to be… – Not a great collection of the best puzzles, since for that we already have the marvelous MATHEON-Kalendar, which now is also available in English – … instead I want to post a – very personal – collection of 23 math diamonds I am in

Every day I hope add a new quiz!… If you feel like, you may post answers on the comments until the 23th!!… And on the 24th I wish to give all the answers!!!

Let´s  ALL Have Wonderful  X-MATHS

Q: This beautiful images show ALL possible Yorgey´s Factorization Diagrams for the number 1155 – there are 16 different diagrams – , for the number 105 – there are 6 diagrams – , and for 15 – there are only 2 – . Can you tell how many different factorization diagrams are there for the number 2016??… Hint: For 2017 there is only one!

Q: Estas hermosas imágines muestran TODOS los posibles Diagramas de Factorización de Yorgey para el número 1155 – que tiene 16 diagramas diferentes – , para el número 105 – que tiene 6 diagramas – , y el número 15 – que tiene sólo 2 – . Puedes decir cuántos diagramas distintos tiene el número 2016??… Pista: Para el 2017 hay sólo uno!

A: 2016 = 2 x 2 x 2 x 2 x 2 x 63 = 2^5  x 63 : Then, since the power of a prime number has a unique diagram – made of “circles of circles of …” of p dots – , and even 2 dots can be thought to be on a circle, then we have only two diagrams!: One is a circle of 63 diagrams of the power 2^5 made of simple dots, and the other is the diagram of 2^5 made of circles of 63 dots each!

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### Author: Math - Update

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