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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 44 · 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 15? (a) 3 (b) 4 (c) 16 (d) 5
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 16 (c) 17 (d) 6
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5
  4. 4.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) 72 (c) 27 (d) 24
  5. 5.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) 16 (b) 51 (c) 48 (d) 144
  6. 6.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) 15 (c) 5 (d) 18
  7. 7.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) 42 (c) 126 (d) 14
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  9. 9.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) 45 (b) 135 (c) 48 (d) 15
  10. 10.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 33 (c) 34 (d) 24
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  12. 12.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) 298 (c) 297 (d) 270
  13. 13.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 432 (c) 366 (d) 442
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  15. 15.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) 6 (c) 54 (d) 18
  16. 16.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 240 (d) 241
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 19 (d) 21
  18. 18.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 176 (c) 166 (d) 184
  19. 19.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 204 (c) 189 (d) 198
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 15 (d) 14
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 3 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  23. 23.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) 13 (c) 42 (d) 39
  24. 24.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 200 (c) 193 (d) 192
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  26. 26.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 172 (c) 154 (d) 163
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  28. 28.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 327 (c) 336 (d) 337
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 8 (c) 7 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  33. 33.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) 51 (b) 153 (c) 17 (d) 54
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
  35. 35.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) 18 (c) 57 (d) 162
  36. 36.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 363 (c) 354 (d) 314
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 3 (b) 5 (c) 4 (d) 6
  38. 38.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) 30 (c) 33 (d) 10
  39. 39.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 588 (c) 470 (d) 598
  40. 40.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 322 (d) 321

Answer key

  1. 4
  2. 16
  3. 4
  4. 24
  5. 48
  6. 15
  7. 42
  8. 17
  9. 45
  10. 33
  11. 18
  12. 297
  13. 441
  14. 6
  15. 18
  16. 240
  17. 20
  18. 175
  19. 198
  20. 14
  21. 4
  22. 4
  23. 39
  24. 192
  25. 17
  26. 163
  27. 5
  28. 336
  29. 8
  30. 7
  31. 16
  32. 16
  33. 51
  34. 18
  35. 54
  36. 363
  37. 5
  38. 30
  39. 597
  40. 321

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