# Lonesum

In appearance, this puzzle looks and feels just like a Kakuro – but there is one small extra rule: a combination of digits forming a sum can only be used once in the grid. For example, if a two-cell 8-sum comprises 3 and 5, then the 3/5 or 5/3 combinations cannot occur in any other two-cell 8-sums in the grid.

This additional constraint creates quite a logically tricky puzzle to both compile – as the size of the grid is limited and, unlike Kakuro, starter digits are often necessary – and to solve.

This puzzle was a regular feature in French puzzle publications 'Eleusis' and 'Logigram<' in the 1980s; it then went on to feature in its own magazine (under its french name) 'Nombres Fléchés'. In the UK, the puzzle appeared in 'Number Corner' and 'Logical Thinker' (which later became 'Logical Puzzles'), under the name Arrownumber, until these magazines closed.

Recently, it has begun to be feature regularly in 'Kakuro' magazine. The puzzle’s original design closely resembled an Arroword. When the grid was changed to look more like a Kakuro puzzle, the arrows were dropped and so was the name. We now call it, the very fitting, Lonesum.

Instructions

Fill the grid so that each sum (block of cells) adds up to the total in the box above or to the left of it. You can only use the digits 1-9 and you must not use the same digit twice in a sum. In addition, a combination of digits forming a sum can only be used once in a grid. For example, if a two-cell 8-sum comprises 3 and 5, then 3/5 or 5/3 cannot appear in any other two-cell 8-sums in the grid.

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