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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 698 · 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 5? (a) 10 (b) 6 (c) 4 (d) 5
  2. 2.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
  3. 3.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 140 (d) 150
  4. 4.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) 57 (b) 18 (c) 54 (d) 162
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 3 (d) 4
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 16 (d) 15
  10. 10.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 130 (d) 129
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 7 (c) 4 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  13. 13.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 53 (d) 62
  14. 14.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 354 (c) 364 (d) 314
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 19 (c) 9 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  18. 18.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) 27 (c) 9 (d) 30
  19. 19.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 356 (d) 426
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 4 (d) 2
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 16 (d) 15
  23. 23.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 52 (c) 43 (d) 44
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 13 (d) 4
  26. 26.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 238 (d) 249
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 18 (d) 17
  29. 29.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  30. 30.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 403 (c) 393 (d) 402
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 13 (c) 15 (d) 14
  32. 32.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) 189 (c) 66 (d) 63
  33. 33.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) 18 (c) 45 (d) 15
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  36. 36.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 246 (c) 247 (d) 237
  37. 37.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 393 (c) 384 (d) 334
  38. 38.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 138 (c) 146 (d) 137
  39. 39.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 436 (c) 537 (d) 547
  40. 40.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 543 (c) 434 (d) 534

Answer key

  1. 5
  2. 339
  3. 149
  4. 54
  5. 6
  6. 19
  7. 5
  8. 4
  9. 15
  10. 129
  11. 6
  12. 3
  13. 53
  14. 363
  15. 18
  16. 20
  17. 4
  18. 27
  19. 426
  20. 3
  21. 3
  22. 15
  23. 43
  24. 20
  25. 14
  26. 249
  27. 9
  28. 18
  29. 8
  30. 402
  31. 14
  32. 63
  33. 15
  34. 4
  35. 20
  36. 246
  37. 393
  38. 137
  39. 546
  40. 543

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