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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 779 · 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 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 357 (c) 366 (d) 367
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 3 (d) 2
  4. 4.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) 340 (c) 298 (d) 339
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  7. 7.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 111 (c) 120 (d) 102
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 7 (c) 6 (d) 4
  9. 9.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 66 (d) 189
  10. 10.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
  11. 11.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 321 (c) 322 (d) 312
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  13. 13.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 89 (c) 90 (d) 80
  14. 14.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 205 (c) 195 (d) 204
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 8 (b) 7 (c) 6 (d) 9
  16. 16.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) 17 (b) 153 (c) 54 (d) 51
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  18. 18.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) 135 (b) 48 (c) 15 (d) 45
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  20. 20.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) 60 (c) 57 (d) 19
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 5 (c) 7 (d) 6
  22. 22.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) 126 (b) 42 (c) 45 (d) 14
  23. 23.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 394 (c) 334 (d) 393
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 15 (d) 17
  26. 26.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 56 (c) 65 (d) 74
  27. 27.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) 27 (b) 9 (c) 30 (d) 81
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 14 (c) 15 (d) 13
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 7 (d) 18
  30. 30.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 381 (c) 382 (d) 326
  31. 31.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 13 (d) 15
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
  34. 34.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) 63 (c) 180 (d) 20
  35. 35.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) 162 (b) 54 (c) 18 (d) 57
  36. 36.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) 282 (c) 260 (d) 283
  37. 37.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  38. 38.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 618 (d) 619
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 4 (b) 15 (c) 14 (d) 16
  40. 40.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) 16 (b) 48 (c) 144 (d) 51

Answer key

  1. 366
  2. 6
  3. 4
  4. 339
  5. 20
  6. 2
  7. 111
  8. 6
  9. 63
  10. 21
  11. 321
  12. 7
  13. 89
  14. 204
  15. 8
  16. 51
  17. 7
  18. 45
  19. 5
  20. 57
  21. 7
  22. 42
  23. 393
  24. 17
  25. 16
  26. 65
  27. 27
  28. 14
  29. 18
  30. 381
  31. 3
  32. 14
  33. 20
  34. 60
  35. 54
  36. 282
  37. 8
  38. 618
  39. 15
  40. 48

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