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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 513 · 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 12? (a) 7 (b) 13 (c) 6 (d) 8
  2. 2.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 118 (c) 126 (d) 108
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  5. 5.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
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 3 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  10. 10.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 130 (d) 140
  11. 11.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 23 (d) 72
  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 4 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 16 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 3 (d) 5
  16. 16.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 381 (c) 372 (d) 326
  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) 400 (c) 493 (d) 492
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  19. 19.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 435 (c) 426 (d) 362
  20. 20.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 108 (c) 98 (d) 107
  21. 21.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
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 19 (d) 20
  23. 23.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 123 (c) 124 (d) 132
  24. 24.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) 430 (c) 537 (d) 528
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 9 (c) 6 (d) 8
  26. 26.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) 24 (b) 216 (c) 72 (d) 75
  27. 27.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) 6 (c) 18 (d) 21
  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) 543 (c) 434 (d) 544
  29. 29.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 364 (c) 314 (d) 363
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 16 (d) 4
  31. 31.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) 33 (b) 99 (c) 36 (d) 11
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 15 (d) 14
  35. 35.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 204 (c) 189 (d) 199
  36. 36.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 439 (d) 438
  37. 37.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) 39 (c) 117 (d) 13
  38. 38.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7

Answer key

  1. 7
  2. 117
  3. 9
  4. 5
  5. 21
  6. 5
  7. 7
  8. 4
  9. 6
  10. 139
  11. 69
  12. 27
  13. 17
  14. 2
  15. 4
  16. 381
  17. 492
  18. 2
  19. 435
  20. 107
  21. 15
  22. 20
  23. 123
  24. 537
  25. 8
  26. 72
  27. 18
  28. 543
  29. 363
  30. 15
  31. 33
  32. 16
  33. 9
  34. 15
  35. 198
  36. 438
  37. 39
  38. 8
  39. 4
  40. 6

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