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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 19 · 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 17? (a) 3 (b) 18 (c) 1 (d) 2
  2. 2.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 109 (c) 110 (d) 100
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  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) 162 (b) 18 (c) 57 (d) 54
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  6. 6.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 84 (d) 75
  7. 7.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) 63 (b) 180 (c) 20 (d) 60
  8. 8.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) 18 (b) 15 (c) 45 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  10. 10.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 282 (c) 291 (d) 266
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
  13. 13.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) 21 (b) 54 (c) 6 (d) 18
  14. 14.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 476 (c) 606 (d) 607
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18
  16. 16.The numbers 8 to 16 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) 12 (c) 36 (d) 108
  17. 17.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 128 (c) 110 (d) 120
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 21
  22. 22.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) 21 (d) 66
  23. 23.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 99 (c) 90 (d) 108
  24. 24.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 636 (c) 496 (d) 627
  25. 25.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) 468 (d) 390
  26. 26.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
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  28. 28.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 208 (c) 195 (d) 204
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 15 (d) 14
  30. 30.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) 45 (b) 135 (c) 15 (d) 48
  31. 31.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
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
  33. 33.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 384 (c) 468 (d) 469
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  35. 35.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 508 (c) 410 (d) 498
  36. 36.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 358 (c) 430 (d) 429
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 7 (c) 17 (d) 18
  38. 38.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 466 (c) 456 (d) 382
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 21 (d) 19
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 13 (b) 14 (c) 9 (d) 11

Answer key

  1. 2
  2. 109
  3. 2
  4. 54
  5. 7
  6. 75
  7. 60
  8. 15
  9. 9
  10. 291
  11. 6
  12. 18
  13. 18
  14. 606
  15. 18
  16. 36
  17. 119
  18. 5
  19. 3
  20. 18
  21. 20
  22. 63
  23. 99
  24. 636
  25. 477
  26. 137
  27. 8
  28. 204
  29. 14
  30. 45
  31. 57
  32. 15
  33. 468
  34. 7
  35. 507
  36. 429
  37. 18
  38. 465
  39. 20
  40. 13

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