Toll

A tower with thirteen hours in its ring and twelve bells to hang in them — six each, weights dealt from one pool, so the hands match and nobody can blame the deal. Hang one bell a turn on any empty hour; when the last bell goes up the peal goes round: every neighbouring pair swings to the HEAVIER side and scores the difference. One hour is left silent all evening and its two edges never pay anybody, so the last hang is choosing what never gets counted. Put your heavies beside their lights, keep your lights at home, and watch a tower that stayed quiet all evening count everything at once.

How it feels

• A tower quiet all evening
• The six going up next to their one
• One hour that never rings

What the design is for

• 01

  The difference is the score

  An edge pays the heavier side exactly the gap: six over two rings four, and equal bells ring for nobody. A heavy beside an equal is worth nothing — placement is the whole game, and the arithmetic is public from the first hang.

• 02

  Thirteen hours, twelve bells

  One hour stays silent, and the two edges that touch it never swing. The odd hour is not decoration. On an EVEN ring the hands match and every hour has an hour opposite it, so the ringer hanging second can answer every bell at the hour across from it — and the peal then rings dead even by arithmetic rather than by play, which the tests build and demonstrate. Thirteen is odd, and no rotation or reflection of an odd ring pairs off every hour, so that answer does not exist. In its place is a decision: the last hang chooses which hour stays quiet, and a light of yours beside their heavy can be left uncounted.

• 03

  The half, and no drawn towers

  The ringer who hangs second holds half a point before a bell goes up, and a half cannot be tied — so every tower here rings for somebody. It replaced a second count on the swings, which used to tie as well.

• 04

  Nothing hidden, nothing rolled

  No luck past the deal and no secret state — the ring, both hands, whose hang it is. The tower is quiet while it fills, and every argument about what it will count can be had out loud, mid-game, with the bells in view.

• 05

  Taught hang by hang

  Six steps: the hang, the swing, lights at home, heavies abroad, the hour you choose to leave silent — and then the whole tower to yourself.