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Induction Problem: Covering a Checkerboard

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Using mathematical induction, prove or disprove that all checkerboards of these shapes can be completely covered using right triominoes whenever n is a positive integer.

a) 3 x 2^n
b) 6 x 2^n
c) 3^n x 3^n
d) 6^n x 6^n

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Solution Summary

This solution uses mathematical induction to prove or disprove that four checkerboards of different dimensions can be completely covered by right triominoes. All calculations are shown.

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Two right triominoes will exactly cover an area of the checkerboard of dimensions 2x3. Therefore, if the total number of squares on the checkerboard is evenly divisible by 6, it will be possible to completely cover the checkerboard with right triominoes.

To use mathematical induction, we first test the case n = 1 and then test the case n + 1. If both cases are true, the statement is proven and the checkerboard can be covered.

a) Using 1:
Number of squares = ...

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