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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 662 · 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.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) 23 (b) 207 (c) 69 (d) 72
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
  3. 3.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 156 (d) 138
  4. 4.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) 24 (c) 72 (d) 216
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  8. 8.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 408 (c) 344 (d) 399
  9. 9.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 157 (c) 158 (d) 148
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  11. 11.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) 45 (c) 5 (d) 18
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 11 (b) 10 (c) 9 (d) 4
  13. 13.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) 466 (d) 465
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  15. 15.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 624 (c) 615 (d) 625
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  18. 18.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 71 (d) 72
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 21
  20. 20.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 44 (c) 52 (d) 43
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  22. 22.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 322 (c) 375 (d) 366
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 18 (d) 17
  24. 24.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) 48 (b) 144 (c) 16 (d) 51
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  26. 26.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 441 (c) 432 (d) 442
  27. 27.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 310 (c) 348 (d) 357
  28. 28.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 366 (c) 367 (d) 357
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 17 (b) 5 (c) 16 (d) 15
  31. 31.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 558 (d) 567
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 8 (b) 5 (c) 6 (d) 7
  33. 33.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 104 (c) 94 (d) 103
  34. 34.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) 24 (b) 8 (c) 72 (d) 27
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 14 (c) 13 (d) 3
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 7 (c) 6 (d) 8
  37. 37.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 6 (b) 7 (c) 8 (d) 9
  39. 39.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17

Answer key

  1. 69
  2. 18
  3. 147
  4. 72
  5. 2
  6. 30
  7. 3
  8. 408
  9. 157
  10. 8
  11. 15
  12. 10
  13. 465
  14. 3
  15. 624
  16. 297
  17. 8
  18. 71
  19. 20
  20. 43
  21. 19
  22. 375
  23. 17
  24. 48
  25. 9
  26. 441
  27. 357
  28. 366
  29. 7
  30. 16
  31. 567
  32. 7
  33. 103
  34. 24
  35. 14
  36. 8
  37. 9
  38. 8
  39. 6
  40. 17

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