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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 622 · 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.

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  1. 1.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 352 (c) 351 (d) 306
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 16 (d) 17
  3. 3.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) 33 (c) 99 (d) 11
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 5 (c) 17 (d) 16
  5. 5.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) 18 (b) 6 (c) 21 (d) 54
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 17 (d) 19
  7. 7.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
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 13 (b) 11 (c) 5 (d) 12
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 20 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  12. 12.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 574 (c) 564 (d) 454
  13. 13.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 405 (c) 406 (d) 342
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
  15. 15.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 68 (d) 86
  16. 16.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 260 (c) 283 (d) 282
  17. 17.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) 30 (b) 10 (c) 33 (d) 90
  18. 18.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 631 (d) 492
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
  21. 21.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 8 (b) 6 (c) 5 (d) 7
  23. 23.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) 9 (c) 27 (d) 30
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  25. 25.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 603 (c) 480 (d) 612
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 14 (c) 15 (d) 16
  27. 27.The numbers 14 to 22 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) 162 (c) 57 (d) 18
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 19 (d) 18
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 21 (d) 9
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  33. 33.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 298 (c) 339 (d) 340
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 18 (d) 19
  35. 35.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) 18 (b) 45 (c) 15 (d) 5
  36. 36.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) 27 (d) 8
  37. 37.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) 36 (b) 12 (c) 108 (d) 39
  38. 38.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 42 (c) 33 (d) 34
  39. 39.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 463 (c) 380 (d) 462
  40. 40.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) 23 (b) 69 (c) 72 (d) 207

Answer key

  1. 351
  2. 16
  3. 33
  4. 16
  5. 18
  6. 18
  7. 45
  8. 12
  9. 3
  10. 19
  11. 2
  12. 573
  13. 405
  14. 18
  15. 77
  16. 282
  17. 30
  18. 630
  19. 18
  20. 18
  21. 5
  22. 7
  23. 27
  24. 4
  25. 612
  26. 15
  27. 54
  28. 15
  29. 19
  30. 4
  31. 20
  32. 5
  33. 339
  34. 18
  35. 15
  36. 24
  37. 36
  38. 33
  39. 462
  40. 69

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