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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 773 · 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 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 484 (c) 609 (d) 619
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 15 (c) 3 (d) 13
  3. 3.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 71 (c) 80 (d) 72
  4. 4.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  5. 5.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 288 (c) 289 (d) 279
  6. 6.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) 57 (d) 60
  7. 7.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 272 (c) 301 (d) 291
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 18 (d) 17
  10. 10.The numbers 16 to 24 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) 20 (c) 63 (d) 180
  11. 11.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 385 (c) 328 (d) 375
  12. 12.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) 144 (b) 48 (c) 51 (d) 16
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 15 (b) 16 (c) 14 (d) 5
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  17. 17.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) 17 (c) 153 (d) 54
  18. 18.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) 72 (b) 24 (c) 8 (d) 27
  19. 19.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) 11 (c) 33 (d) 99
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  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) 381 (b) 390 (c) 391 (d) 332
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  23. 23.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 106 (c) 97 (d) 88
  24. 24.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) 15 (d) 45
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 15 (b) 6 (c) 16 (d) 17
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 17 (d) 15
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 15 (d) 17
  28. 28.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) 24 (c) 63 (d) 21
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 5 (b) 8 (c) 6 (d) 7
  30. 30.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) 22 (c) 69 (d) 66
  31. 31.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 295 (c) 294 (d) 285
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 6 (d) 7
  33. 33.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) 108 (b) 39 (c) 36 (d) 12
  34. 34.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) 75 (c) 24 (d) 72
  35. 35.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 519 (c) 418 (d) 520
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 17 (c) 8 (d) 18
  37. 37.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 139 (d) 148
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 4 (b) 7 (c) 6 (d) 5
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  40. 40.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 558 (c) 559 (d) 444

Answer key

  1. 618
  2. 14
  3. 71
  4. 9
  5. 288
  6. 57
  7. 300
  8. 2
  9. 17
  10. 60
  11. 384
  12. 48
  13. 7
  14. 2
  15. 15
  16. 20
  17. 51
  18. 24
  19. 33
  20. 6
  21. 390
  22. 4
  23. 97
  24. 45
  25. 16
  26. 16
  27. 16
  28. 21
  29. 7
  30. 66
  31. 294
  32. 7
  33. 36
  34. 72
  35. 519
  36. 18
  37. 139
  38. 6
  39. 4
  40. 558

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