Sorry, no online dictionaries contain the exact phrase arithmetical puzzle.
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Reverse dictionary results:
1. logic
 2. cipher
3. example
4. figure
5. sum
6. summing
7. add
8. algebra
9. average
10. borrow
 11. calculation
12. cast
13. computation
14. divide
15. educated
16. mean
17. number
18. numbering
19. numbing
20. plus
 21. real
22. zero
23. alu
24. graphic
25. means
26. program
27. clue
28. fiver
29. hint
30. solve
 31. stick
32. sticks
33. work
34. addition
35. address
36. addressing
37. algorithm
38. answer
39. answering
40. bate

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You can look up the words in the phrase individually using these links:   arithmetical ?   puzzle ?
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arit*to search for words beginning with arit, or
*zzleto search for words ending with zzle
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