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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 254 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 3 (b) 5 (c) 6 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  6. 6.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 174 (c) 183 (d) 192
  7. 7.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 49 (c) 58 (d) 50
  8. 8.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 21 (c) 63 (d) 189
  9. 9.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 21 (d) 6
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
  11. 11.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 132 (c) 141 (d) 150
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 7 (c) 5 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  14. 14.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 57 (c) 54 (d) 162
  15. 15.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 582 (d) 466
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 7 (d) 17
  17. 17.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 625 (d) 624
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  19. 19.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 13 (d) 39
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  21. 21.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 402 (c) 496 (d) 495
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  24. 24.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 406 (d) 396
  25. 25.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 66 (d) 22
  26. 26.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 140 (d) 149
  27. 27.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 57 (d) 19
  28. 28.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 86 (c) 85 (d) 76
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 4 (d) 5
  30. 30.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 432 (c) 541 (d) 540
  31. 31.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 534 (c) 535 (d) 428
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  33. 33.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 550 (c) 438 (d) 540
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 18 (d) 9
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 3 (d) 13
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  37. 37.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 153 (c) 17 (d) 54
  38. 38.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 195 (c) 205 (d) 208
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 19 (d) 8
  40. 40.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 303 (c) 294 (d) 304

Answer key

  1. 4
  2. 2
  3. 9
  4. 5
  5. 8
  6. 183
  7. 49
  8. 63
  9. 18
  10. 6
  11. 141
  12. 7
  13. 3
  14. 54
  15. 591
  16. 17
  17. 624
  18. 4
  19. 39
  20. 5
  21. 495
  22. 15
  23. 7
  24. 405
  25. 66
  26. 149
  27. 57
  28. 85
  29. 4
  30. 540
  31. 534
  32. 8
  33. 549
  34. 19
  35. 14
  36. 5
  37. 51
  38. 204
  39. 18
  40. 303

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