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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 474 · 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.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 216 (d) 75
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 15 (c) 4 (d) 14
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 14 (d) 13
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 8 (b) 6 (c) 7 (d) 9
  5. 5.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) 22 (d) 66
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 4 (d) 16
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 16 (d) 6
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 15 (b) 14 (c) 13 (d) 6
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 7 (b) 19 (c) 17 (d) 18
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 7 (b) 6 (c) 5 (d) 8
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  14. 14.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 48 (d) 45
  15. 15.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
  16. 16.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) 60 (b) 19 (c) 57 (d) 171
  17. 17.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 348 (d) 357
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 3 (d) 5
  19. 19.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 411 (c) 346 (d) 412
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 3 (d) 2
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 16 (d) 14
  22. 22.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 621 (c) 486 (d) 622
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 18 (c) 17 (d) 7
  24. 24.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 288 (c) 315 (d) 324
  25. 25.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 366 (c) 376 (d) 375
  26. 26.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 240 (c) 252 (d) 253
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 2 (c) 4 (d) 3
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 8 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  32. 32.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 561 (c) 452 (d) 570
  33. 33.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 242 (c) 256 (d) 246
  34. 34.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 498 (c) 640 (d) 630
  35. 35.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 123 (c) 124 (d) 132
  36. 36.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 14 (c) 42 (d) 126
  37. 37.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 195 (c) 208 (d) 204
  38. 38.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  40. 40.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 96 (d) 105

Answer key

  1. 72
  2. 15
  3. 14
  4. 8
  5. 66
  6. 2
  7. 6
  8. 15
  9. 17
  10. 14
  11. 18
  12. 7
  13. 6
  14. 45
  15. 33
  16. 57
  17. 357
  18. 5
  19. 411
  20. 3
  21. 15
  22. 621
  23. 18
  24. 324
  25. 375
  26. 252
  27. 5
  28. 3
  29. 4
  30. 19
  31. 7
  32. 570
  33. 255
  34. 639
  35. 123
  36. 42
  37. 204
  38. 5
  39. 9
  40. 105

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