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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 814 · 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 11? (a) 7 (b) 9 (c) 12 (d) 8
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  3. 3.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) 216 (c) 72 (d) 24
  4. 4.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 53 (d) 62
  5. 5.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) 51 (d) 54
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 6 (b) 7 (c) 8 (d) 9
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  11. 11.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) 129 (c) 120 (d) 130
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 4 (c) 16 (d) 14
  13. 13.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 369 (c) 370 (d) 360
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 17 (d) 7
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 17 (d) 19
  16. 16.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 235 (d) 234
  17. 17.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) 7 (b) 24 (c) 63 (d) 21
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 13 (d) 14
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 17 (d) 18
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 21
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 8 (c) 9 (d) 7
  22. 22.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 177 (c) 186 (d) 178
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 5 (d) 15
  24. 24.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 516 (c) 507 (d) 517
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  27. 27.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) 15 (b) 18 (c) 5 (d) 45
  28. 28.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 544 (c) 434 (d) 543
  29. 29.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 282 (c) 315 (d) 306
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 3 (c) 15 (d) 13
  31. 31.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 579 (c) 464 (d) 588
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 8 (b) 7 (c) 5 (d) 6
  33. 33.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 178 (c) 169 (d) 170
  34. 34.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 47 (c) 38 (d) 48
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 9 (d) 20
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 12 (b) 14 (c) 5 (d) 13
  37. 37.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
  38. 38.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 55 (c) 46 (d) 64
  39. 39.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
  40. 40.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 492 (c) 621 (d) 631

Answer key

  1. 8
  2. 3
  3. 72
  4. 53
  5. 51
  6. 8
  7. 3
  8. 16
  9. 9
  10. 19
  11. 129
  12. 15
  13. 369
  14. 18
  15. 18
  16. 234
  17. 21
  18. 14
  19. 18
  20. 20
  21. 8
  22. 177
  23. 16
  24. 516
  25. 18
  26. 2
  27. 15
  28. 543
  29. 315
  30. 14
  31. 588
  32. 7
  33. 169
  34. 47
  35. 19
  36. 13
  37. 48
  38. 55
  39. 18
  40. 630

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