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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 738 · 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 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 10 (c) 11 (d) 7
  2. 2.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 523 (d) 420
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  4. 4.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 23 (d) 72
  5. 5.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) 90 (b) 10 (c) 33 (d) 30
  6. 6.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) 412 (c) 411 (d) 346
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 7 (b) 9 (c) 11 (d) 12
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  10. 10.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 586 (b) 462 (c) 576 (d) 585
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  12. 12.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 621 (d) 612
  13. 13.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) 14 (b) 126 (c) 45 (d) 42
  14. 14.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) 54 (c) 153 (d) 17
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 6 (c) 5 (d) 7
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  17. 17.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 270 (c) 279 (d) 280
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 9 (b) 7 (c) 8 (d) 6
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 14 (b) 12 (c) 13 (d) 3
  21. 21.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 501 (d) 406
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9
  23. 23.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 196 (c) 202 (d) 186
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  25. 25.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 588 (c) 464 (d) 589
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  27. 27.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) 216 (b) 72 (c) 75 (d) 24
  28. 28.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
  29. 29.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
  30. 30.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) 15 (b) 48 (c) 135 (d) 45
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  32. 32.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 149 (c) 158 (d) 150
  33. 33.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 546 (c) 442 (d) 556
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 18 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  37. 37.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) 24 (b) 63 (c) 21 (d) 7
  38. 38.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 268 (c) 285 (d) 294
  39. 39.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 60 (d) 52
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 16 (d) 17

Answer key

  1. 10
  2. 522
  3. 5
  4. 69
  5. 30
  6. 411
  7. 11
  8. 6
  9. 9
  10. 585
  11. 4
  12. 621
  13. 42
  14. 51
  15. 7
  16. 8
  17. 279
  18. 3
  19. 8
  20. 13
  21. 501
  22. 19
  23. 195
  24. 7
  25. 588
  26. 3
  27. 72
  28. 39
  29. 66
  30. 45
  31. 9
  32. 149
  33. 555
  34. 2
  35. 19
  36. 8
  37. 21
  38. 294
  39. 51
  40. 16

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