Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 X 2 tile with a missing 1 x 1 square) such that there is exactly a single 1 x 1 square missing from any chosen square. A successful tiling for n = 2 and specifically the top-right square chosen is shown as an example: (But to verify that it is always possible to tile for any chosen square to be missing would require 16 examples.) Prove by Mathematical Induction that Hugh will always be able to perform this tiling on a 2" x 2" board for any chosen 1 × 1 square missing.
Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 X 2 tile with a missing 1 x 1 square) such that there is exactly a single 1 x 1 square missing from any chosen square. A successful tiling for n = 2 and specifically the top-right square chosen is shown as an example: (But to verify that it is always possible to tile for any chosen square to be missing would require 16 examples.) Prove by Mathematical Induction that Hugh will always be able to perform this tiling on a 2" x 2" board for any chosen 1 × 1 square missing.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(c) Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 x 2 tile with
a missing 1 x 1 square) such that there is exactly a single 1 x 1 square missing from any
chosen square. A successful tiling for n = 2 and specifically the top-right square chosen is
shown as an example:
(But to verify that it is always possible to tile for any chosen square to be missing would require
16 examples.)
Prove by Mathematical Induction that Hugh will always be able to perform this tiling on a
2" x 2" board for any chosen 1 x 1 square missing.
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