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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 700 · 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 two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  2. 2.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) 66 (d) 22
  3. 3.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 74 (c) 92 (d) 84
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 14 (d) 15
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  6. 6.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
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
  8. 8.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 618 (d) 619
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  10. 10.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) 11 (b) 33 (c) 99 (d) 36
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 6 (b) 5 (c) 7 (d) 8
  12. 12.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) 30 (b) 81 (c) 27 (d) 9
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 16 (d) 14
  14. 14.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 433 (c) 360 (d) 423
  15. 15.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 96 (c) 78 (d) 87
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  17. 17.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 493 (c) 400 (d) 492
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
  19. 19.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 424 (c) 354 (d) 423
  20. 20.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) 12 (c) 39 (d) 36
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 17 (b) 18 (c) 16 (d) 7
  22. 22.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
  23. 23.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 414 (c) 514 (d) 504
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 5 (c) 4 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  28. 28.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 185 (c) 186 (d) 194
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 15 (c) 4 (d) 16
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 7 (c) 12 (d) 13
  31. 31.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) 21 (c) 63 (d) 7
  32. 32.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 140 (d) 148
  33. 33.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 516 (c) 416 (d) 507
  34. 34.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 384 (c) 385 (d) 375
  35. 35.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 60 (d) 50
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 18 (d) 7
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 15 (c) 17 (d) 16
  38. 38.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 152 (c) 161 (d) 162
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 14 (d) 16
  40. 40.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 177 (c) 168 (d) 178

Answer key

  1. 6
  2. 66
  3. 83
  4. 15
  5. 8
  6. 39
  7. 18
  8. 618
  9. 9
  10. 33
  11. 7
  12. 27
  13. 15
  14. 432
  15. 87
  16. 3
  17. 492
  18. 15
  19. 423
  20. 36
  21. 17
  22. 207
  23. 513
  24. 4
  25. 4
  26. 7
  27. 9
  28. 185
  29. 15
  30. 12
  31. 21
  32. 139
  33. 516
  34. 384
  35. 59
  36. 18
  37. 16
  38. 161
  39. 15
  40. 177

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