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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 164 · 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 times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 2 (d) 3
  2. 2.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 30 (d) 9
  3. 3.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 438 (d) 439
  4. 4.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) 54 (b) 21 (c) 18 (d) 6
  5. 5.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 172 (c) 154 (d) 163
  6. 6.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 230 (c) 237 (d) 238
  7. 7.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 38 (c) 48 (d) 56
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 9 (d) 20
  11. 11.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 310 (d) 309
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 2 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  14. 14.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) 36 (b) 99 (c) 33 (d) 11
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 3 (c) 15 (d) 14
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 21 (c) 9 (d) 19
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 16 (d) 17
  20. 20.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 8 (d) 72
  21. 21.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 210 (c) 220 (d) 219
  22. 22.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) 48 (c) 15 (d) 45
  23. 23.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) 19 (c) 60 (d) 57
  24. 24.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) 13 (c) 39 (d) 42
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 5 (d) 2
  26. 26.The numbers 12 to 20 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) 48 (c) 144 (d) 16
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 19 (d) 17
  28. 28.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 472 (d) 601
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 16 (b) 4 (c) 14 (d) 15
  31. 31.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 324 (c) 325 (d) 288
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  33. 33.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 199 (c) 198 (d) 204
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
  35. 35.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 477 (c) 486 (d) 396
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 5 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
  40. 40.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 106 (c) 124 (d) 116

Answer key

  1. 4
  2. 27
  3. 438
  4. 18
  5. 163
  6. 237
  7. 47
  8. 3
  9. 7
  10. 19
  11. 309
  12. 4
  13. 6
  14. 33
  15. 2
  16. 9
  17. 14
  18. 20
  19. 16
  20. 24
  21. 219
  22. 45
  23. 57
  24. 39
  25. 4
  26. 48
  27. 18
  28. 600
  29. 8
  30. 15
  31. 324
  32. 5
  33. 198
  34. 4
  35. 486
  36. 5
  37. 6
  38. 3
  39. 3
  40. 115

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