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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 483 · 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 12? (a) 8 (b) 13 (c) 6 (d) 7
  2. 2.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) 21 (c) 18 (d) 6
  3. 3.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) 171 (b) 57 (c) 60 (d) 19
  4. 4.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) 390 (c) 381 (d) 332
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 18 (d) 9
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 9 (b) 11 (c) 6 (d) 12
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  8. 8.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 498 (c) 499 (d) 489
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 13 (c) 11 (d) 14
  10. 10.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 210 (c) 212 (d) 211
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  13. 13.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) 63 (b) 20 (c) 60 (d) 180
  14. 14.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 170 (c) 152 (d) 162
  15. 15.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) 162 (b) 54 (c) 18 (d) 57
  16. 16.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) 72 (d) 27
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 3 (c) 14 (d) 13
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 7 (d) 4
  19. 19.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 120 (d) 110
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 4 (d) 2
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 2 (d) 3
  24. 24.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 360 (c) 370 (d) 369
  25. 25.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 150 (c) 132 (d) 142
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 4 (c) 3 (d) 5
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 19 (d) 9
  28. 28.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) 39 (b) 42 (c) 117 (d) 13
  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) 33 (b) 36 (c) 11 (d) 99
  30. 30.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) 63 (d) 7
  31. 31.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 207 (c) 198 (d) 208
  32. 32.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 459 (c) 384 (d) 468
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 17 (b) 15 (c) 5 (d) 16
  34. 34.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) 18 (c) 15 (d) 5
  35. 35.The numbers 11 to 19 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) 15 (c) 135 (d) 45
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  37. 37.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) 72 (c) 207 (d) 69
  38. 38.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) 153 (b) 51 (c) 17 (d) 54
  39. 39.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 302 (c) 345 (d) 346
  40. 40.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 176 (c) 186 (d) 185

Answer key

  1. 7
  2. 18
  3. 57
  4. 390
  5. 19
  6. 11
  7. 8
  8. 498
  9. 13
  10. 210
  11. 5
  12. 4
  13. 60
  14. 161
  15. 54
  16. 24
  17. 14
  18. 6
  19. 119
  20. 5
  21. 9
  22. 3
  23. 4
  24. 369
  25. 141
  26. 5
  27. 20
  28. 39
  29. 33
  30. 21
  31. 207
  32. 468
  33. 16
  34. 15
  35. 45
  36. 8
  37. 69
  38. 51
  39. 345
  40. 185

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