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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 627 · 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 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 140 (c) 122 (d) 131
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 19 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  4. 4.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 145 (c) 136 (d) 146
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 18 (d) 8
  6. 6.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 438 (c) 439 (d) 429
  7. 7.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 50 (c) 41 (d) 32
  8. 8.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 105 (c) 114 (d) 96
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  10. 10.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 476 (d) 606
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 15 (b) 6 (c) 16 (d) 17
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  14. 14.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 280 (d) 303
  15. 15.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) 16 (c) 48 (d) 51
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  17. 17.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) 57 (c) 18 (d) 162
  18. 18.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 195 (c) 204 (d) 208
  19. 19.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 360 (c) 361 (d) 351
  20. 20.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) 20 (b) 60 (c) 63 (d) 180
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 4 (d) 3
  23. 23.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) 72 (c) 24 (d) 216
  24. 24.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) 63 (b) 7 (c) 21 (d) 24
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 6 (c) 5 (d) 7
  26. 26.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 416 (c) 517 (d) 507
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  28. 28.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) 36 (c) 12 (d) 39
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 14 (c) 15 (d) 13
  30. 30.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) 33 (c) 11 (d) 36
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 6 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 5 (c) 15 (d) 17
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  36. 36.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
  37. 37.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) 24 (b) 27 (c) 72 (d) 8
  38. 38.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 62 (d) 70
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 4 (d) 16
  40. 40.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) 42 (b) 117 (c) 13 (d) 39

Answer key

  1. 131
  2. 18
  3. 3
  4. 145
  5. 19
  6. 438
  7. 41
  8. 105
  9. 19
  10. 606
  11. 3
  12. 16
  13. 9
  14. 312
  15. 48
  16. 7
  17. 54
  18. 204
  19. 360
  20. 60
  21. 2
  22. 5
  23. 72
  24. 21
  25. 7
  26. 516
  27. 8
  28. 36
  29. 14
  30. 33
  31. 18
  32. 6
  33. 8
  34. 16
  35. 5
  36. 15
  37. 24
  38. 61
  39. 15
  40. 39

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