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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 57 · 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 times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  2. 2.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 537 (c) 430 (d) 528
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  4. 4.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 594 (d) 468
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  7. 7.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 294 (c) 324 (d) 334
  8. 8.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 165 (c) 166 (d) 174
  9. 9.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) 618 (c) 484 (d) 619
  10. 10.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 270 (c) 271 (d) 252
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 2 (d) 5
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  13. 13.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 176 (c) 166 (d) 184
  14. 14.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  15. 15.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) 72 (c) 75 (d) 24
  16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 274 (d) 303
  17. 17.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) 60 (b) 171 (c) 19 (d) 57
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 4 (c) 16 (d) 14
  19. 19.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) 283 (d) 260
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  21. 21.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) 189 (b) 63 (c) 66 (d) 21
  22. 22.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 427 (d) 426
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 15 (d) 17
  24. 24.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) 41 (c) 50 (d) 32
  25. 25.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) 51 (b) 48 (c) 144 (d) 16
  26. 26.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) 54 (b) 21 (c) 18 (d) 6
  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) 162 (b) 18 (c) 57 (d) 54
  28. 28.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 90 (d) 80
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  30. 30.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) 39 (b) 42 (c) 13 (d) 117
  31. 31.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 420 (c) 411 (d) 352
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 19 (c) 8 (d) 18
  33. 33.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 134 (d) 144
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  35. 35.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 460 (d) 459
  36. 36.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  37. 37.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
  38. 38.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) 24 (d) 21
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 9 (b) 8 (c) 7 (d) 6
  40. 40.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 477 (c) 390 (d) 468

Answer key

  1. 20
  2. 537
  3. 5
  4. 594
  5. 8
  6. 7
  7. 333
  8. 165
  9. 618
  10. 270
  11. 4
  12. 20
  13. 175
  14. 7
  15. 72
  16. 303
  17. 57
  18. 15
  19. 282
  20. 6
  21. 63
  22. 426
  23. 16
  24. 41
  25. 48
  26. 18
  27. 54
  28. 89
  29. 4
  30. 39
  31. 420
  32. 19
  33. 143
  34. 2
  35. 459
  36. 3
  37. 60
  38. 21
  39. 8
  40. 477

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