Puzzles
Here is a 5 × 5 grid. Eight of its cells hold an algebraic expression in two unknown real numbers, a and b. Rows and columns are numbered 0–4 from the top-left.
col 0 col 1 col 2 col 3 col 4
+----------+----------+----------+----------+----------+
row 0 | | | | | |
+----------+----------+----------+----------+----------+
row 1 | 1 - b | | -ab | b/(a-1) | |
+----------+----------+----------+----------+----------+
row 2 | | | | | a^b + 2 |
+----------+----------+----------+----------+----------+
row 3 | | (1-b)/a | | | |
+----------+----------+----------+----------+----------+
row 4 | b^2 + 1 | 1/a | | 2 - 2b | |
+----------+----------+----------+----------+----------+Rules
- Put positive integers in some of the cells and leave the others empty. For some N, the grid must contain exactly one 1, two 2's, three 3's, …, and N N's, and no other numbers.
- For each K, the cells labeled K must form one orthogonally connected region (a "K-omino").
- For each K > 1, the K-omino must contain a copy of the (K−1)-omino's shape. The copy may be rotated or reflected.
- Each cell with an expression must be filled, and its label must equal the value of that expression. The same a and b are used everywhere.
After you complete the grid, add up the labels in each row. Empty cells count as 0.
Answer format: a single integer, (largest row sum) × (smallest row sum).
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