Pipsum – a number puzzle made of pips

How it works

Pipsum follows the rules of Kakuro, the Japanese cross-sums puzzle — with one difference that makes a lot of things easier: the only values are 1 to 6, not 1 to 9. So there is little arithmetic and a lot of inference.

Some cells are blocked, and some of those carry sums: the number at the top right applies to the free cells to its right, the number at the bottom left to the free cells below it. One such unbroken run of free cells is called a block. Tap a free cell, then the pip count below; tapping a filled cell clears it again.

• Every block adds up to exactly its sum. No more, no less.
• Within a block no pip count appears twice. Across block boundaries it may very well — that is the most common mistake early on.

On this page Pipsum starts in practice mode: the puzzle type is already selected, so you choose Easy, Medium or Hard and begin. Play as many grids as you like. None of it is scored, and the clock counts upwards — it is a mirror, not a time limit. Every puzzle has exactly one solution and can be solved without guessing. Pipsum also appears in Endless, in Deduction Rush and in duels.

Tips & techniques

• Decomposition. Some sums can be made in only one way for their length: 3 over two cells is always 1+2, 11 over two cells always 5+6. Which value goes where is still open — which two they are is settled. No block has more than three decompositions, at any length.
• Remainder. When a block has just one empty cell left, its value is the sum minus what is already there. No searching, just a subtraction — and the most common step of all.
• Crossing. Every free cell belongs to one block across and one block down. Only what is possible in both remains possible: if one allows just 5 or 6 there and the other just 2 or 6, the cell has to be a 6. This is the technique that sets Pipsum apart from an arithmetic exercise.
• Block exclusion. A pip count that fits into none of a block's remaining decompositions is ruled out for all of its cells — even if no single cell forbids it directly.
• Five-cell blocks are a gift. A block over five cells holds five different pip counts out of six. Exactly one is missing, and the sum gives it away: 21 minus the sum of the block.
• Trial. On Hard only: put a pip count in tentatively. If it leads to a contradiction, it was the wrong one.
• Start at the extremes. Very small and very large sums have the fewest decompositions. That is where something is settled soonest, and from there the remainder and the crossing carry you further.

Frequently asked questions

Do I need to be good at mental arithmetic?

No. With values from 1 to 6 the sums stay small, and no block can be split in more than three ways. The difficulty never lies in the arithmetic but in which blocks cross where.

Can the same pip count appear twice in one row?

Yes, as long as the two cells belong to different blocks. Repeats are only forbidden within a block. A blocked cell in between starts a new block.

How do the difficulty levels differ?

Easy is a 4×4 grid that needs only decomposition and the remainder. Medium is played on 5×5 and adds the crossing. Hard is a 6×6 grid with longer blocks, including one or two five-cell blocks as a way in; there you may need block exclusion and at most one trial.

Are there hints?

In practice mode, yes. A hint shows the next cell that can be deduced for certain — it never reveals the pip count itself. You get three hints per puzzle on Easy, two on Medium and one on Hard.

Does Pipsum cost anything, and do I need an account?

No. Pipsum runs free of charge in your browser, and you can play at once without signing up.