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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 170 · 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.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 126 (c) 135 (d) 144
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 6 (b) 18 (c) 16 (d) 17
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 6 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  7. 7.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
  8. 8.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 30 (c) 90 (d) 10
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 1 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  12. 12.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) 7 (b) 63 (c) 21 (d) 24
  13. 13.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) 540 (c) 550 (d) 438
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  15. 15.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 39 (c) 48 (d) 40
  16. 16.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  17. 17.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 195 (c) 186 (d) 202
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 6 (d) 5
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
  21. 21.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 391 (c) 381 (d) 332
  22. 22.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) 39 (b) 42 (c) 13 (d) 117
  23. 23.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) 69 (b) 198 (c) 66 (d) 22
  24. 24.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 144 (c) 152 (d) 134
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  26. 26.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 12 (d) 36
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 4 (d) 3
  28. 28.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) 8 (c) 24 (d) 72
  29. 29.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 408 (c) 417 (d) 350
  30. 30.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 114 (d) 124
  31. 31.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 452 (d) 571
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 5 (d) 6
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 13 (d) 14
  35. 35.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 178 (c) 188 (d) 187
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 15
  39. 39.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 110 (d) 120
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 5 (b) 17 (c) 15 (d) 16

Answer key

  1. 135
  2. 17
  3. 9
  4. 6
  5. 6
  6. 2
  7. 15
  8. 30
  9. 3
  10. 8
  11. 7
  12. 21
  13. 549
  14. 5
  15. 39
  16. 9
  17. 195
  18. 6
  19. 5
  20. 20
  21. 390
  22. 39
  23. 66
  24. 143
  25. 2
  26. 36
  27. 4
  28. 24
  29. 417
  30. 123
  31. 570
  32. 6
  33. 4
  34. 14
  35. 187
  36. 17
  37. 18
  38. 16
  39. 119
  40. 16

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