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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 363 · 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 14? (a) 5 (b) 15 (c) 6 (d) 4
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 4 (d) 6
  3. 3.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 612 (c) 486 (d) 622
  4. 4.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 493 (b) 400 (c) 483 (d) 492
  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) 51 (b) 54 (c) 153 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  7. 7.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 220 (c) 219 (d) 218
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  9. 9.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) 8 (b) 24 (c) 27 (d) 72
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 15 (c) 14 (d) 16
  11. 11.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 158 (d) 166
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 5 (d) 16
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 18 (d) 6
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 15 (d) 14
  16. 16.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
  17. 17.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 298 (d) 270
  18. 18.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 284 (c) 309 (d) 319
  19. 19.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
  20. 20.The numbers 6 to 14 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) 33 (c) 90 (d) 10
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 15 (b) 14 (c) 8 (d) 12
  22. 22.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) 38 (c) 48 (d) 47
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 18 (d) 20
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 3 (d) 13
  25. 25.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) 117 (c) 13 (d) 39
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  28. 28.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 320 (c) 372 (d) 373
  29. 29.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 349 (c) 339 (d) 304
  30. 30.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 138 (c) 137 (d) 128
  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) 19 (c) 57 (d) 171
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 18 (d) 16
  34. 34.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 180 (c) 198 (d) 190
  35. 35.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 104 (c) 95 (d) 96
  36. 36.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 454 (c) 374 (d) 453
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  38. 38.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) 18 (b) 57 (c) 162 (d) 54
  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) 18 (c) 6 (d) 21
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3

Answer key

  1. 5
  2. 5
  3. 621
  4. 492
  5. 51
  6. 8
  7. 219
  8. 9
  9. 24
  10. 15
  11. 157
  12. 5
  13. 16
  14. 17
  15. 14
  16. 42
  17. 297
  18. 318
  19. 123
  20. 30
  21. 14
  22. 47
  23. 19
  24. 14
  25. 39
  26. 20
  27. 2
  28. 372
  29. 348
  30. 137
  31. 57
  32. 5
  33. 17
  34. 189
  35. 95
  36. 453
  37. 4
  38. 54
  39. 18
  40. 3

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