PuzzlesNumber Theory
Fill every white cell of the 5×5 grid below with a digit from 1 to 9 (no zeros).
Each clue gives either the sum or the product of the digits in its entry, and you have to work out which. A clue may fit both readings if the sum and the product of the entry happen to be equal. Digits may repeat within an entry, and two entries may have the same value.
c1 c2 c3 c4 c5
+----+----+----+----+----+
r1 | 1 | 2 |####| 3 | 4 |
+----+----+----+----+----+
r2 | 5 | | 6 | | |
+----+----+----+----+----+
r3 |####| 7 | | |####|
+----+----+----+----+----+
r4 | 8 | | | | 9 |
+----+----+----+----+----+
r5 | 10 | |####| 11 | |
+----+----+----+----+----+#### marks a black square. An entry is a maximal run of two or more white cells, read left to right (Across) or top to bottom (Down), and its clue number sits in its first cell.
| Across | cells | clue | Down | cells | clue | |
|---|---|---|---|---|---|---|
| 1A | r1 c1–c2 | 2 | 1D | c1 r1–r2 | 7 | |
| 3A | r1 c4–c5 | 14 | 2D | c2 r1–r5 | 21 | |
| 5A | r2 c1–c5 | 28 | 3D | c4 r1–r5 | 9 | |
| 7A | r3 c2–c4 | 6 | 4D | c5 r1–r2 | 40 | |
| 8A | r4 c1–c5 | 63 | 6D | c3 r2–r4 | 24 | |
| 10A | r5 c1–c2 | 40 | 8D | c1 r4–r5 | 14 | |
| 11A | r5 c4–c5 | 7 | 9D | c5 r4–r5 | 13 |
The solution is unique and can be reached by pure deduction.
Answer format: give the sum of all 21 digits in the completed grid, as a single integer.
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