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It has been some time since I read about it and I find it difficult to find a reference for it but I recall Conway asked, if we call a triangular array of hexagons with $n$ hexagons along its sides $T_n$, which $T_n$ can be tiled by copies of $T_2$, which he named "tribones"?

The answer was some condition on $n$ modulo 12, proved via "Tiling Groups", but he remarkably showed that this result couldn't obtained through any colouring argument!

EDIT: It appears to be mentioned in this overview of tiling results and they provide a helpful illustration:

$T_9$" />

The condition is $T_n$ can be tiled iff $n=0,2,9,11$ modulo 12.

It has been some time since I read about it and I find it difficult to find a reference for it but I recall Conway asked, if we call a triangular array of hexagons with $n$ hexagons along its sides $T_n$, which $T_n$ can be tiled by copies of $T_2$, which he named "tribones"?

The answer was some condition on $n$ modulo 12, proved via "Tiling Groups", but he remarkably showed that this result couldn't obtained through any colouring argument!

EDIT: It appears to be mentioned in this overview of tiling results and they provide a helpful illustration:

The condition is $T_n$ can be tiled iff $n=0,2,9,11$ modulo 12.

It has been some time since I read about it and I find it difficult to find a reference for it but I recall Conway asked, if we call a triangular array of hexagons with $n$ hexagons along its sides $T_n$, which $T_n$ can be tiled by copies of $T_3$, which he named "tribones"?

The answer was some condition on $n$ modulo 12, proved via "Tiling Groups", but he remarkably showed that this result couldn't obtained through any colouring argument!

EDIT: It appears to be mentioned in this overview of tiling results and they provide a helpful illustration:

$T_9$" />

The condition is $T_n$ can be tiled iff $n=0,2,9,11$ modulo 12.

It has been some time since I read about it and I find it difficult to find a reference for it but I recall Conway asked, if we call a triangular array of hexagons with $n$ hexagons along its sides $T_n$, which $T_n$ can be tiled by copies of $T_2$, which he named "tribones"?

The answer was some condition on $n$ modulo 12, proved via "Tiling Groups", but he remarkably showed that this result couldn't obtained through any colouring argument!

EDIT: It appears to be mentioned in this overview of tiling results and they provide a helpful illustration:

$T_9$" />

The condition is $T_n$ can be tiled iff $n=0,2,9,11$ modulo 12.

It has been sometime and I find it difficult to find a reference for it but I recall Conway asked, if we call a triangular array of hexagons with $n$ hexagons along its sides $T_n$, which $T_n$ can be tiled by copies of $T_3$, which he named "tribones"?

The answer was some condition on $n$ modulo 12, proved via "Tiling Groups", but he remarkably showed that this result couldn't obtained through any colouring argument!

EDIT: It appears to be mentioned in this overview of tiling results and they provide a helpful illustration:

$T_9$" />

The condition is $T_n$ can be tiled iff $n=0,2,9,11$ modulo 12.

It has been some time since I read about it and I find it difficult to find a reference for it but I recall Conway asked, if we call a triangular array of hexagons with $n$ hexagons along its sides $T_n$, which $T_n$ can be tiled by copies of $T_3$, which he named "tribones"?

The answer was some condition on $n$ modulo 12, proved via "Tiling Groups", but he remarkably showed that this result couldn't obtained through any colouring argument!

EDIT: It appears to be mentioned in this overview of tiling results and they provide a helpful illustration:

$T_9$" />

The condition is $T_n$ can be tiled iff $n=0,2,9,11$ modulo 12.