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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 684 · 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 11? (a) 12 (b) 7 (c) 9 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 13 (c) 3 (d) 14
  4. 4.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 63 (d) 21
  5. 5.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 237 (c) 246 (d) 247
  6. 6.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) 45 (b) 14 (c) 42 (d) 126
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 15 (c) 14 (d) 13
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  9. 9.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) 117 (b) 42 (c) 13 (d) 39
  10. 10.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 34 (c) 44 (d) 43
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 14 (b) 4 (c) 15 (d) 13
  12. 12.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) 10 (c) 90 (d) 33
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  14. 14.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) 66 (b) 69 (c) 198 (d) 22
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 19 (d) 18
  16. 16.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) 16 (c) 48 (d) 144
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 20 (d) 19
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 4 (d) 3
  19. 19.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) 45 (b) 5 (c) 18 (d) 15
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  22. 22.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 68 (d) 58
  23. 23.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 489 (c) 498 (d) 404
  24. 24.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 144 (c) 143 (d) 134
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 6 (b) 5 (c) 7 (d) 8
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 12 (b) 10 (c) 9 (d) 13
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 17 (b) 15 (c) 5 (d) 16
  29. 29.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 597 (d) 588
  30. 30.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 96 (d) 86
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 5 (d) 17
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
  33. 33.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 436 (c) 537 (d) 546
  34. 34.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 146 (c) 128 (d) 137
  35. 35.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) 33 (b) 99 (c) 36 (d) 11
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 20 (d) 19
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 7 (b) 6 (c) 8 (d) 5
  38. 38.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) 60 (c) 180 (d) 63
  39. 39.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 318 (c) 360 (d) 369
  40. 40.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) 21 (b) 24 (c) 7 (d) 63

Answer key

  1. 8
  2. 4
  3. 14
  4. 63
  5. 246
  6. 42
  7. 14
  8. 4
  9. 39
  10. 43
  11. 14
  12. 30
  13. 8
  14. 66
  15. 18
  16. 48
  17. 19
  18. 5
  19. 15
  20. 3
  21. 9
  22. 67
  23. 498
  24. 143
  25. 7
  26. 5
  27. 12
  28. 16
  29. 597
  30. 95
  31. 16
  32. 15
  33. 546
  34. 137
  35. 33
  36. 19
  37. 7
  38. 60
  39. 369
  40. 21

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