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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 97 · 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) 6 (c) 4 (d) 15
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  3. 3.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) 21 (c) 7 (d) 63
  4. 4.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 276 (c) 267 (d) 256
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 8 (c) 7 (d) 6
  7. 7.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 188 (c) 179 (d) 170
  8. 8.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) 27 (d) 72
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 5
  10. 10.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 102 (c) 110 (d) 101
  11. 11.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) 18 (d) 6
  12. 12.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) 51 (b) 48 (c) 16 (d) 144
  13. 13.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 56 (c) 65 (d) 74
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 18 (d) 20
  15. 15.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) 216 (b) 75 (c) 24 (d) 72
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 4 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  18. 18.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 387 (d) 336
  19. 19.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) 90 (b) 10 (c) 30 (d) 33
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 5 (b) 4 (c) 6 (d) 7
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 20 (d) 18
  23. 23.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 564 (c) 454 (d) 573
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 4 (d) 5
  26. 26.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 489 (c) 499 (d) 404
  27. 27.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 184 (c) 175 (d) 166
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 4 (d) 2
  29. 29.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) 36 (b) 99 (c) 33 (d) 11
  30. 30.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 78 (c) 87 (d) 96
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  32. 32.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 50 (d) 32
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  35. 35.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 494 (c) 633 (d) 624
  36. 36.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) 57 (c) 18 (d) 162
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  39. 39.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 410 (c) 507 (d) 498
  40. 40.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 234 (d) 225

Answer key

  1. 5
  2. 4
  3. 21
  4. 276
  5. 8
  6. 7
  7. 179
  8. 24
  9. 4
  10. 101
  11. 18
  12. 48
  13. 65
  14. 19
  15. 72
  16. 5
  17. 7
  18. 396
  19. 30
  20. 6
  21. 6
  22. 19
  23. 573
  24. 20
  25. 4
  26. 498
  27. 175
  28. 4
  29. 33
  30. 87
  31. 8
  32. 41
  33. 18
  34. 5
  35. 633
  36. 54
  37. 3
  38. 4
  39. 507
  40. 234

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