Here is one Crossnumber puzzle. In addition to the regular rules, no walls have been placed in the grid: recovering the walls’ positions is part of the puzzle. All cells form a single connected region; as usual, all straight runs of two or more cells are clued (but no run of a single cell is), with clue numbers increasing from left to right and from top to bottom.
Across: 2. All its digits are equal. 4. One less than a multiple of 11. 5. A cube read backwards. 8. The sum of its digits is 11. 9. A pentagonal number.
Down: 1. Its digits form an increasing geometric progression with an integer common ratio. 2. A triangular number. 3. One more than a multiple of 11. 4. Its digits form an increasing arithmetic progression with common difference equal to one. 6. A Fibonacci number. 7. A prime.