Love For MathCreative Math Education

Challenge 2: Painting tiles, no two black together

We have some tiles (in a row) and we need to paint them. We have 2 colors, yellow and black.

Rules:

  1. You cannot place 2 black tiles together.
  2. You can use any number of black or yellow tiles.



Example: 3 tiles can be painted in the following 5 ways.
YYY, YBY, BYB, BYY, YYB


Can you find how many ways are there to paint 5 tiles?

What students worked out4

  • Student 1

    This is what I found out it follows the Fibonacci scheme like in the last problem 8+5.

  • Student 3

    13 POSSIBILITIES
    YYYYY
    YYYYB
    YYYBY
    YYBYY
    YBYYY
    BYYYY
    YYBYB
    YBYYB
    BYYYB
    YBYBY
    BYYBY
    BYBYY
    BYBYB

  • Student 8

    13

  • Student 6

    YYYYY,
    YYYYB
    YYYBY
    YYBYY
    YBYYY
    BYYYY
    YYBYB
    YBYYB
    BYYYB
    YBYBY
    BYYBY
    BYBYY
    BYBYB