Bimble path-finding techniques

This guide assumes you know the rules from how to play Bimble. Squares are named row first, then column, counting from the top left.

Think in links, not in walks

Our solver never draws the walk from the start. It looks at every pair of neighbouring squares with no hedge between them, which we call a link, and decides one at a time whether the walk uses it or not. That is the trick worth copying. Drawing from stone 1 forces you to choose at every fork; deciding links lets you work on whichever part of the field is easiest, and the pieces join up later. The game only lets you draw from stone 1, so keep the pieces in your head or on paper and draw once they connect.

Count the ways in and out

Every square needs exactly two links: one in and one out. The two exceptions are stone 1 and the last stone, which need exactly one. Most of every solve is this count, applied over and over.

• A corner square has only two links, so the walk uses both, unless it holds stone 1 or the last stone.
• An edge square with a hedge beside it is in the same position: two links left, both used.
• Once a square has its two links, every other link it has is ruled out, and that often leaves a neighbour with only two.
• Stone 1 and the last stone each need just one link, so a corner holding one of them is not settled by the count alone.

Stone order: the idea Easy fields lean on

Our generator only publishes an Easy field if the solve needs the stone-order and no-loop idea at least ten times, so it pays to be quick at it. Three rules cover it.

• Two stones side by side can only be linked if their numbers are consecutive. Stone 8 next to stone 3 is a wall.
• More generally, any piece of walk you have worked out must pass its stones in a run of consecutive numbers, in one direction. A piece holding 8 then 9 cannot be joined to stone 1.
• Stone 1 and the last stone are the two ends of the walk, so a link that would join the piece holding stone 1 to the piece holding the last stone is wrong, unless every square is already on it. And a link that joins the two ends of the same piece would close a loop.

Worked example: Bimble No. 3

Bimble No. 3 (an Easy 6x6 from Tuesday 27 October) has stone 9, the last stone, in the top left corner, stone 8 to its right in row 1 column 2, and stone 3 next to that in row 1 column 3. Stone 1 is in row 3 column 2, just below. There are no hedges. Here is how the top left corner falls.

1. Stones 8 and 3 are neighbours but not consecutive, so the link between row 1 columns 2 and 3 is ruled out.
2. Stone 8 now has only two links left: left to stone 9 and down to row 2 column 2. It needs two, so it uses both. The walk goes into 9 from 8.
3. Stone 9 is the last stone and needs just one link, which it now has. Its other link, down to row 2 column 1, is ruled out.
4. Row 2 column 1 has lost its link upwards, so only two remain: right to row 2 column 2 and down to row 3 column 1. Both are used.
5. Row 2 column 2 now has its two links (up to stone 8 and left to row 2 column 1), so its links right and down are ruled out.
6. The piece now runs row 3 column 1, row 2 column 1, row 2 column 2, stone 8, stone 9. Stone 1 sits right next to its end at row 3 column 1, but joining them would put stone 1 straight before stone 8. Ruled out by stone order.

So the walk ends by climbing the left edge to stones 8 and 9, known before drawing a single step. Meanwhile stone 3 has lost its link to 8, so it uses its other two, and the other three corners each use both of their links. The full walk is on the Bimble No. 3 answer page.

Stiles and oaks

A stile uses two links on one straight line through its square. An oak uses one link across and one up or down. Both get much stronger next to an edge or a hedge, because those remove links.

• A stile on the edge of the field cannot run straight off the board, so it must run along the edge. Its link inwards is ruled out. In Bimble No. 7 the stile in row 1, column 6 settles this way: the walk crosses it from side to side.
• A stile with a hedge on one side cannot use that line at all, so it goes the other way, and both links on the other line are used.
• An oak on the edge (not in a corner) has only one link on the line going inwards, so it must use it, plus one of its two links along the edge.
• An oak with a hedge on one side must use the opposite link on that line.
• Once you know one link of a stile, you know the other. Once you know one link of an oak, its opposite is ruled out.

Our generator never puts a stile or oak on a square with only two open sides, where it would say nothing, and it removes every one the field can do without. So every clue on a Hard or Ramble field matters: if you have not used one yet, look at it now.

A colouring check

This one is not in our solver, but it is true and sometimes handy. Colour the field like a chessboard. Every step changes colour, so a stretch of walk between two squares of the same colour always takes an even number of steps, and between different colours an odd number. A 7x7 field has 25 squares of the corner colour and 24 of the other, so a walk through all 49 must start and finish on the corner colour. When you are weighing up a route between two consecutive stones, count it: if the stones are the same colour and your route takes an odd number of steps, it is not the route.

Bottlenecks

If part of the field can only be reached through one link, the walk must use it. Our solver checks for this, but it is rare: none of the first nine daily fields needed it. It is still worth a glance at a corner fenced off by a hedge, because a pocket with only two ways in, and neither end stone inside it, must use both.

What if, on Hard and Ramble days

Easy fields never need a what-if, and Medium fields at most one. Hard and Ramble fields are different: our generator only publishes a Hard field if it needs at least one, and a Ramble at least two. The caps keep them fair: a Hard field allows up to four, each found within 18 deductions, and a Ramble up to six, each within 20. Bimble No. 7 needed two, of 6 and 5 steps.

• Choose a link next to a stile, oak or hedge, or a link that decides which way a narrow corridor runs. Those set off forced moves quickly.
• Assume the link is used (or not used) and follow only forced moves: the count, stone order, stiles and oaks.
• Stop when a square has fewer than two possible links left, a loop closes, or stones meet out of order. Then the opposite of your assumption is true.
• If twenty or so forced steps pass with no trouble, abandon it and try another link.

Quick checklist

• Settle every corner and every hedged edge square first.
• Rule out links between neighbouring stones that are not consecutive.
• Grow pieces of walk anywhere, and check each new link for loops and stone order.
• Read every stile and oak, especially on an edge or beside a hedge. Every one is needed.
• Use chessboard colours to check whether a route between two stones has the right length.
• Only then try a what-if, starting next to a clue.

Ready to try it? Play today's Bimble, or replay finished fields from the Bimble answers archive. To see how we make sure every field has exactly one walk, read logic puzzles you never have to guess.