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#213 Cross sward

Set by Howard Williams

Older age does bring some benefits. My daughters Kate and Laura have offered to help me by taking on the maintenance of my garden, which is rectangular with a small, rectangular vegetable plot in one corner. The remainder is lawn.

To make it fair for them, I have agreed that my last job in the garden will be to partition it into two with a straight fence, with each daughter getting the same area.

Kate suggested that we forget about the vegetable plot, and only divide the lawn. She sketched a line on the diagram that would give them each exactly half the lawn (with no awkward pinch point to get the mower through). Laura, meanwhile, drew a fence that would divide the lawn and the vegetable patch into halves. To make their lines, neither daughter needed to measure anything, they just needed a straight edge.

Can you draw the lines on which Kate and Laura propose to build fences?

Solution next week

#212 Sound off

Solution

Seven presses is the maximum. As there are three remotes that can each be muted or unmuted, there are 2 x 2 x 2 = 8 possible states. If we say 0 is off and 1 is on, then, to start with, the remotes could be in any of the states shown below (aside from 111). The diagram shows a path through the states by changing one remote at a time, where the worst-case scenario is that Sam鈥檚 mum starts at 101 and it takes her seven steps to get all three remotes to 111.