Consider the following grid of streets with roadblocks:


If you are facing in the direction of the arrow and want to get to the dot, the highlighted path is the shortest:


This traces out an L.

Let's try another one:


This traces out the symbol @.

Design such a grid so that all the digits 0 through 9 can be displayed in such a way, by choosing a starting intersection and direction, and a finishing intersection. There must be exactly one shortest path between these points, starting in the direction of the arrow. The 'best' grid has the least amount of blocks, because the destruction of natural environments by cities is already a big enough problem.

However, in accordance with @humn's bounty, please do post answers that might win the honorary 'architectural' prize.

Rotating the street grid is permitted when making your character, reflecting is not. U-turns aren't allowed. Your grid is permitted to have columns/rows with varying height/width as long as it still forms a grid.

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    $\begingroup$ How are characters with discontiguous regions ( " = % ! and the like) supposed to work? Are U-turns allowed? $\endgroup$
    – Rubio
    Jan 16, 2017 at 1:13
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    $\begingroup$ Either way, this sounds way too tedious and seems more like manual labor than a puzzle to enjoy. Just imagine designing x, X, &, *, and then differentiate between `, ",", ".", '... $\endgroup$ Jan 16, 2017 at 2:56
  • $\begingroup$ Yes, this sounds too ambitious and not much fun. The scope is too great. Maybe tracing all ten digits can be fun, but all 90-something characters on a keyboard? That's a slog. (I think this puzzle is the wrong way round. It could work if the map and some starting and end points were given and they spelled out a message.) $\endgroup$
    – M Oehm
    Jan 16, 2017 at 6:22
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    $\begingroup$ Thank you for your suggestions everyone, I've made the puzzle only the digits so that it's better. $\endgroup$
    – boboquack
    Jan 16, 2017 at 6:32
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    $\begingroup$ @Wen1now i.stack.imgur.com/4cNPm.png $\endgroup$
    – boboquack
    Jan 16, 2017 at 6:47

1 Answer 1


The planning commission’s present road map for the future (revised) has 7 streets with 4 roadblocks bounding 6 city blocks.

Please forgive the gap in 6 if, as it seems, 4 and 8 must have gaps anyway in any configuration where they have unique shortest paths.

To be sure, the numbers looked better in the previous plan with 8 streets and 9 city blocks.   Worth noting that 0, 1, 5, 6, 7, 8 and 9 only require the 6 streets and 3 city blocks on the west side of town.


  • 1
    $\begingroup$ Unequally spaced streets are alright. Good job! $\endgroup$
    – boboquack
    Jan 16, 2017 at 22:07
  • $\begingroup$ Got some new ideas thanks to you, @boboquack. Also haven't yet given up on a crazy 45-degree-rotated 8 $\endgroup$
    – humn
    Jan 16, 2017 at 22:43
  • $\begingroup$ Civic Environmental Panel was glad to see another 3 blocks spared, @boboquack, now down to 6 if it passes spec $\endgroup$
    – humn
    Jan 17, 2017 at 14:03
  • $\begingroup$ Yes, this is good! I think this is the minimum, unless you can do a 2x2 or a 1xN<=5. If no other answers pop up, I'll accept this 19/1 UTC time. $\endgroup$
    – boboquack
    Jan 17, 2017 at 21:07
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    $\begingroup$ I for one prefer the numbers in the 9 block solution. The 3 in the 6 block solution is not very crisp. Maybe with some different spacings $\endgroup$
    – Trenin
    Jan 18, 2017 at 16:13

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