Math Is Fun Forum

shaoen01

Member

Registered: 2008-01-26

Posts: 18

Using Mathematical induction

Hi all,

Previously, i asked what a tromino is and i worked some equations out. However, i am not sure if my proof is right. So if someone can help me take a look and point out to me my mistake would be fantastic.

Qns 1:
Use mathematical induction to prove that for any integer n more than and equals to 1, if one square is removed from a 2^n x 2^n checkerboard, the remaining squares can be covered by an L-Tromino.

My workings:
A tromino consists of 3 small squares.

So i let P(n) = (2^n x 2^n)-1 for n>=1--> Because the qns says 1 square is removed.

Basis step:
P(1)=(2x2)-1
      = 3 --> Which is true.

Inductive Hypothesis:
So i am now supposed to prove P(n+1)=

x

is true.

So by multiplication definition (i think):
n=dq for some integer q
And d (divisor)=3 since a L-tromino has 3 squares.
n=3q

is an integer because the product or multiplication of an integer is still an integer. And because the divisor is 3, the above workings proved that the remaining squares can be covered by a L-tromino.

Last edited by shaoen01 (2008-02-27 19:40:42)