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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 858 · 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 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 14 (c) 13 (d) 3
  2. 2.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) 13 (b) 39 (c) 117 (d) 42
  3. 3.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 66 (c) 69 (d) 198
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  5. 5.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 312 (c) 286 (d) 322
  6. 6.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 255 (c) 246 (d) 256
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 19 (d) 7
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 9 (b) 15 (c) 12 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 4 (d) 5
  12. 12.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 382 (c) 465 (d) 466
  13. 13.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) 430 (c) 358 (d) 429
  14. 14.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 402 (d) 486
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 17 (d) 18
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 19 (d) 7
  19. 19.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 73 (c) 82 (d) 74
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 19 (d) 17
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 3 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  23. 23.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 16 (d) 18
  26. 26.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 24 (d) 72
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  28. 28.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 102 (d) 101
  29. 29.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 291 (c) 300 (d) 272
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 6 (c) 5 (d) 3
  31. 31.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) 20 (c) 180 (d) 60
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 4 (d) 6
  33. 33.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 482 (c) 615 (d) 616
  34. 34.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) 54 (b) 18 (c) 162 (d) 57
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 5 (d) 4
  37. 37.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) 57 (b) 60 (c) 19 (d) 171
  38. 38.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 45 (d) 36
  39. 39.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 489 (c) 398 (d) 480
  40. 40.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) 27 (b) 81 (c) 30 (d) 9

Answer key

  1. 14
  2. 39
  3. 66
  4. 7
  5. 321
  6. 255
  7. 2
  8. 18
  9. 14
  10. 7
  11. 4
  12. 465
  13. 429
  14. 495
  15. 19
  16. 8
  17. 18
  18. 18
  19. 73
  20. 18
  21. 5
  22. 9
  23. 258
  24. 18
  25. 17
  26. 24
  27. 3
  28. 101
  29. 300
  30. 5
  31. 60
  32. 6
  33. 615
  34. 54
  35. 9
  36. 5
  37. 57
  38. 45
  39. 489
  40. 27

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