Ideas from mathematics and logic, taught by the ghosts with a board diagram for each. In the app, one new tip arrives for each day you play.

1. Reading the board, and your tools

1. 1The opening algorithmOpenings are routine — think later!
2. 2Watch the numbers that only shrink…watch what only shrinks… less work…
3. 3Count from the other side…never count ghosts around a 7… hunt the ×…
4. 4Pins bookmark your assumptionLong-press 📌 — plant it at the root!
5. 5Lines have a flip side too…for big rows, count the × instead…
6. 6Corners are dense with information…corners cannot lie…
7. 7Deductions fall like dominoesOne domino falls — and the far ones topple!

2. Comparing clues, and using hints

1. 8Read the hint's reasonT-take the reason, not the answer…!
2. 9Where no clue can seeS-some cells no clue can see…
3. 10The law of overlapping windows…only compare with the neighbors…
4. 11The inclusion argument…when one fits inside the other… you win…
5. 12Find it by subtracting…neighbors are for subtracting…
6. 13Lines and clues share one shape…clues are not the only pairs…
7. 14The pigeonhole principleThey can't BOTH fit…!? Then it's decided!

3. Counting and checking

1. 15Sanity checks: catch errors earlyThe earlier the catch, the cheaper the fix!
2. 16Count the ways…just count the ways… while still awake…
3. 17Erase the finished clues…erase the finished ones… so restful…
4. 18Inclusion–exclusion…subtract the overlap… THE formula…
5. 19Case analysis: two worlds…in or out… keep only what holds both ways…
6. 20Double counting…rows and columns share one purse…
7. 21Think in ranges per room…every room has a capacity…

4. Advanced techniques, and what the marks mean

1. 22Solving by substitution…easy equation first, then substitute…
2. 23Recheck only the cross and windowsOne find — patrol just the cross!
3. 24Postpone the coin flips…cannot decide? then do not… strategy…
4. 25Proof by contradictionI-if I put it here… whoa, contradiction!? …that IS the answer!
5. 26Assume at the busy crossingWrong spot… and nothing happens at all…
6. 27Being true and being provableA lucky guess… still doesn't count…!
7. 28Assumptions on the second floorS-sometimes… you want to prove it yourself… without a hint…

▶ Try 50 rounds in your browser A free demo, no install. All 2,000 rounds are in the app.