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Tromping Games: Tiling with Trominoes
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Published/Copyright:
June 4, 2011
Abstract
The game of Domineering is a combinatorial game that has been solved for several boards, including the standard 8 × 8 board. We create new partizan – and some impartial – combinatorial games by using trominoes instead of and along with dominoes. We analyze these Tromping games for some small boards providing a dictionary of values. Further, we prove properties that permit expressing some connected boards as sums of smaller subboards. We also show who can win in Tromping for some boards of the form m × n, for m = 2, 3, 4, 5 and infinitely many n.
Received: 2011-01-25
Revised: 2010-08-26
Accepted: 2010-08-28
Published Online: 2011-06-04
Published in Print: 2011-June
© de Gruyter 2011
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Articles in the same Issue
- Preface
- On the Intersections of Fibonacci, Pell, and Lucas Numbers
- Proving Balanced T2 and Q2 Identities Using Modular Forms
- Sum-Product Inequalities with Perturbation
- Power Totients with Almost Primes
- On the Sum of Reciprocals of Amicable Numbers
- Tromping Games: Tiling with Trominoes
- There are No Multiply-Perfect Fibonacci Numbers
- Large Zero-Free Subsets of ℤ/pℤ
Articles in the same Issue
- Preface
- On the Intersections of Fibonacci, Pell, and Lucas Numbers
- Proving Balanced T2 and Q2 Identities Using Modular Forms
- Sum-Product Inequalities with Perturbation
- Power Totients with Almost Primes
- On the Sum of Reciprocals of Amicable Numbers
- Tromping Games: Tiling with Trominoes
- There are No Multiply-Perfect Fibonacci Numbers
- Large Zero-Free Subsets of ℤ/pℤ
