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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 32 · 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 6? (a) 5 (b) 6 (c) 7 (d) 10
  2. 2.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) 20 (b) 180 (c) 63 (d) 60
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 15 (d) 14
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  7. 7.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 294 (c) 295 (d) 268
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 19 (d) 20
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  10. 10.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 235 (c) 225 (d) 228
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  12. 12.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 567 (c) 450 (d) 568
  13. 13.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) 117 (c) 42 (d) 39
  14. 14.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) 18 (b) 21 (c) 6 (d) 54
  15. 15.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 336 (c) 397 (d) 396
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 4 (b) 5 (c) 2 (d) 3
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 9 (d) 19
  18. 18.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 60 (c) 70 (d) 78
  19. 19.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 90 (d) 80
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 17 (d) 16
  22. 22.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 152 (c) 162 (d) 161
  23. 23.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
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 18 (d) 7
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  26. 26.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) 69 (b) 66 (c) 22 (d) 198
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 3 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  29. 29.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 58 (c) 40 (d) 49
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 6 (c) 5 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  33. 33.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) 63 (b) 7 (c) 24 (d) 21
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 6 (d) 7
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 5 (b) 6 (c) 4 (d) 3
  36. 36.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 386 (c) 472 (d) 462
  37. 37.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 124 (d) 114
  38. 38.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 332 (c) 381 (d) 390
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 6 (b) 7 (c) 8 (d) 5

Answer key

  1. 6
  2. 60
  3. 14
  4. 5
  5. 8
  6. 4
  7. 294
  8. 20
  9. 3
  10. 234
  11. 2
  12. 567
  13. 39
  14. 18
  15. 396
  16. 4
  17. 20
  18. 69
  19. 89
  20. 7
  21. 17
  22. 161
  23. 157
  24. 18
  25. 20
  26. 66
  27. 4
  28. 4
  29. 49
  30. 18
  31. 5
  32. 9
  33. 21
  34. 6
  35. 5
  36. 471
  37. 123
  38. 390
  39. 4
  40. 7

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