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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 314 · 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 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 3 (c) 13 (d) 12
  2. 2.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) 33 (d) 36
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 8 (b) 6 (c) 7 (d) 5
  5. 5.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 364 (d) 439
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 5 (d) 3
  8. 8.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) 309 (c) 278 (d) 310
  9. 9.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) 75 (b) 24 (c) 72 (d) 216
  10. 10.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 45 (d) 18
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18
  12. 12.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) 54 (b) 153 (c) 51 (d) 17
  13. 13.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 7 (d) 63
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 20 (d) 8
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 15 (d) 14
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  18. 18.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) 126 (b) 42 (c) 14 (d) 45
  19. 19.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 4 (b) 6 (c) 5 (d) 3
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 4 (c) 5 (d) 3
  22. 22.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 66 (c) 74 (d) 56
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 6 (d) 4
  24. 24.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 92 (d) 101
  25. 25.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 211 (c) 212 (d) 201
  26. 26.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 492 (c) 406 (d) 502
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 8 (b) 16 (c) 14 (d) 17
  29. 29.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 286 (c) 285 (d) 276
  30. 30.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 241 (d) 240
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  33. 33.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 594 (d) 595
  34. 34.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 266 (c) 292 (d) 282
  35. 35.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) 48 (b) 135 (c) 45 (d) 15
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 14 (d) 4
  38. 38.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 190 (d) 189
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 1 (d) 2

Answer key

  1. 12
  2. 33
  3. 7
  4. 7
  5. 438
  6. 17
  7. 4
  8. 309
  9. 72
  10. 15
  11. 19
  12. 51
  13. 21
  14. 19
  15. 4
  16. 15
  17. 4
  18. 42
  19. 81
  20. 5
  21. 4
  22. 65
  23. 6
  24. 101
  25. 210
  26. 501
  27. 2
  28. 16
  29. 285
  30. 240
  31. 17
  32. 9
  33. 594
  34. 291
  35. 45
  36. 15
  37. 15
  38. 189
  39. 20
  40. 3

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