Sum Select: choose what to leave out.
Turn a large target into a smaller omission sum, check six worked answers, and distinguish fewer omissions from fewer selected tiles.
A Sum Select target can look awkward when it needs several numbers. Instead of asking only which tiles to include, you can ask which tiles to leave out. Add all nine values, subtract the target, and search for that smaller amount among the excluded tiles.
This is a different way to describe the same answer. The included group and the excluded group partition the board: every tile belongs to exactly one of them. It can make a large target easier to inspect, although it does not necessarily produce the answer with the fewest selected tiles.
Start with a board whose total you can verify
Use this paper exercise with a target of 22. Name rows A, B, and C from top to bottom, and columns 1–3 from left to right. A1 is the 9; B1 and B2 are two different tiles showing 2.
9 7 6 2 2 1 1 1 1
The row totals are 22, 5, and 3. Add them to get 30. If the selected tiles must total 22, the omitted tiles must total 30 − 22 = 8.
Why? The selected total equals the whole-board total minus the omitted total. Leaving out 8 therefore leaves 22. You still need to use actual tile positions: a number value cannot be removed twice unless two separate tiles have that value.
Build one answer by omitting two tiles
Leave out A3, the 6, and B1, the first 2. Their sum is 8. Keep every other tile:
9 7 · · 2 1 1 1 1
The dots mean omitted tiles, not tiles with a value of zero. Verify the included group directly: 9 + 7 + 2 + 1 + 1 + 1 + 1 = 22. The subtraction and the direct addition agree, which gives you two checks on the same proposed answer.
In the live game, select those seven retained tiles and choose Check sum. There is no button that selects “everything except” a group. This is a planning method, not a shortcut in the interface, and the game does not load this fixed paper board. Apply the calculation to the values and target that actually appear.
Find all six two-tile omissions
No tile shows 8, so one omission cannot leave the target of 22. For a pair totaling 8, check the complementary values and their physical locations:
- A2 with B3: 7 + 1 = 8.
- A2 with C1: another 7 + 1 = 8.
- A2 with C2: another 7 + 1 = 8.
- A2 with C3: another 7 + 1 = 8.
- A3 with B1: 6 + 2 = 8.
- A3 with B2: the other 6 + 2 = 8.
These are exactly six pairs. A 9 is already too large to be part of an omission sum of 8 because all values are positive. The remaining smaller pairs cannot make 8. Each listed omitted pair produces a different seven-tile selection, even when the arithmetic uses the same values.
When recording an answer, write the omitted coordinates as well as the numbers. “Leave out a 2” does not say whether B1 or B2 should be excluded; those choices retain different tiles.
Fewest omissions is not fewest selected tiles
The two-tile omissions above are as short as possible, but they retain seven tiles. A much shorter selected answer is the whole top row: 9 + 7 + 6 = 22. Its omitted group is all six lower-row tiles, totaling 2 + 2 + 1 + 1 + 1 + 1 = 8.
That three-tile answer is also the shortest selected answer on this board. The two largest values, 9 and 7, add to only 16, so no one- or two-tile selection can reach 22. The three top-row tiles do reach it.
Complementing a selection exchanges its size with the size of its omitted group. On a nine-tile board, omitting two means selecting seven; omitting six means selecting three. Minimizing the number of omitted tiles therefore goes in the opposite direction from minimizing the number selected. The game accepts any nonempty selection with the exact target; it does not require either minimum.
Use the smaller sum when it helps
For this example, searching for an omitted total of 8 is convenient because every value greater than 8 can immediately be ruled out of that group. On another board, the target itself may be simpler. If the target is 5, for example, the two 2 tiles and any one 1 make it directly. Working backward from 30 would mean describing a much larger excluded total of 25.
Compare the target with the whole-board total minus the target, then choose the description that is easier to verify. Neither approach eliminates the need to inspect tile availability. A small amount can still need several tiles, and a large amount can have an obvious short answer.
Self-check: change the omissions
Keep the target at 22. Does omitting A3 and B2 still work?
Yes. A3 is 6 and B2 is a different physical 2, so the omitted sum is still 8 and the selected sum is still 22. B1 remains selected instead of B2. This is another of the six valid omitted pairs, not a reuse of the same tile.
Use a new paper target of 18. Leave out A1, B1, and B3. Which tiles remain?
The omitted values are 9 + 2 + 1 = 12, so the retained sum is 30 − 12 = 18. Keep A2, A3, B2, C1, C2, and C3: 7 + 6 + 2 + 1 + 1 + 1 = 18. This target is compatible with the game’s three-tile construction too: A1, A2, and B1 make 9 + 7 + 2 = 18.
A useful check before submitting
Write three amounts: the whole-board total, the omitted total, and their difference. Then directly add the selected values. If the results disagree, check whether you included an omitted tile, skipped a retained tile, or reused a coordinate.
All values in Sum Select are positive. That makes omission totals larger than the whole-board total impossible, and it lets you rule out oversized individual tiles. The current game generates each target from three distinct positions, so an answer already exists. This method helps describe and verify another answer; it does not diagnose a new kind of impossible round.