# Posts Tagged: nimbers

• games

## How to win transfinite Nimbers?

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Last time we introduced the game of transfinite Nimbers and asked a winning move for the transfinite game with stones a at position $~(2,2)$, b at $~(4,\omega)$, c at $~(\omega+2,\omega+3)$ and d at position $~(\omega+4,\omega+1)$. Above is the unique winning move : we remove stone d and by the rectangle-rule add… Read more »

• games

## n-dimensional and transfinite Nimbers

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Today, we will expand the game of Nimbers to higher dimensions and do some transfinite Nimber hacking. In our identification between $\mathbb{F}_{16}^*$ and 15-th roots of unity, the number 8 corresponds to $\mu^6$, whence $\sqrt{8}=\mu^3=14$. So, if we add a stone at the diagonal position (14,14) to the Nimbers-position of last time… Read more »

• games

## How to play Nimbers?

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Nimbers is a 2-person game, winnable only if you understand the arithmetic of the finite fields $\mathbb{F}_{2^{2^n}}$ associated to Fermat 2-powers. It is played on a rectangular array (say a portion of a Go-board, for practical purposes) having a finite number of stones at distinct intersections. Here’s a typical position The players alternate making… Read more »