Henry Ernest Dudeney/Puzzles and Curious Problems/175 - Cross-Number Puzzle

by : $175$

 * Cross-Number Puzzle
 * Here is a cross-number puzzle on lines similar to those of the familiar crossword puzzle.
 * The puzzle is to place numbers in the spaces across and down, so as to satisfy the following conditions:


 * Dudeney-Puzzles-and-Curious-Problems-175.png


 * Across:
 * 1. a square number
 * 4. a square number
 * 5. a square number
 * 8. the digits sum to $35$
 * 11. square root of $39$ across
 * 13. a square number
 * 14. a square number
 * 15. square of $36$ across
 * 17. square of half $11$ across
 * 18. three similar figures
 * 19. product of $4$ across and $33$ across
 * 21. a square number
 * 22. five times $5$ across
 * 23. all digits alike, except the central one
 * 25. square of $2$ down
 * 27. see $20$ down
 * 28. a fourth power
 * 29. sum of $18$ across and $31$ across
 * 31. a triangular number
 * 33. one more than $4$ times $36$ across
 * 34. digits sum to $18$, and the three middle numbers are $3$
 * 36. an odd number
 * 37. all digits even, except one, and their sum is $29$
 * 39. a fourth power
 * 40. a cube number
 * 41. twice a square


 * Down:
 * 1. reads both ways alike
 * 2. square root of $28$ across
 * 3. sum of $17$ across and $21$ across
 * 4. digits sum to $19$
 * 5. digits sum to $26$
 * 6. sum of $14$ across and $33$ across
 * 7. a cube number
 * 9. a cube number
 * 10. a square number
 * 12. digits sum to $30$
 * 14. all similar figures
 * 16. sum of digits is $2$ down
 * 18. all similar digits except the first, which is $1$
 * 20. sum of $17$ across and $27$ across
 * 21. a multiple of $19$
 * 22. a square number
 * 24. a square number
 * 26. square of $18$ across
 * 28. a fourth power of $4$ across
 * 30. a triangular number
 * 32. digits sum to $20$ and end with $8$
 * 34. six times $21$ across
 * 35. a cube number
 * 37. a square number
 * 38. a cube number