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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 479 · 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 times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 20 (d) 19
  2. 2.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) 57 (b) 171 (c) 60 (d) 19
  3. 3.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) 369 (d) 370
  4. 4.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
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 18 (b) 16 (c) 7 (d) 17
  6. 6.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) 24 (b) 72 (c) 75 (d) 216
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  8. 8.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) 15 (b) 135 (c) 48 (d) 45
  9. 9.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) 33 (b) 30 (c) 90 (d) 10
  10. 10.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) 42 (b) 45 (c) 14 (d) 126
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  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) 48 (b) 16 (c) 51 (d) 144
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 4 (c) 5 (d) 2
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  16. 16.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 441 (c) 432 (d) 366
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  18. 18.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 59 (c) 50 (d) 68
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
  20. 20.The numbers 8 to 16 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) 12 (c) 36 (d) 108
  21. 21.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 415 (c) 405 (d) 414
  22. 22.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) 207 (b) 69 (c) 23 (d) 72
  23. 23.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  24. 24.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 357 (c) 348 (d) 310
  25. 25.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 612 (c) 622 (d) 621
  26. 26.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 122 (d) 132
  27. 27.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 466 (c) 465 (d) 456
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
  30. 30.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 309 (c) 318 (d) 284
  31. 31.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) 21 (b) 189 (c) 63 (d) 66
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 9 (b) 21 (c) 20 (d) 19
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  34. 34.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) 24 (c) 7 (d) 21
  35. 35.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
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 5 (b) 4 (c) 3 (d) 2
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 5 (d) 3
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 7 (c) 5 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18

Answer key

  1. 19
  2. 57
  3. 369
  4. 54
  5. 17
  6. 72
  7. 8
  8. 45
  9. 30
  10. 42
  11. 4
  12. 48
  13. 5
  14. 4
  15. 4
  16. 441
  17. 7
  18. 59
  19. 15
  20. 36
  21. 414
  22. 69
  23. 9
  24. 357
  25. 621
  26. 131
  27. 465
  28. 2
  29. 19
  30. 318
  31. 63
  32. 20
  33. 6
  34. 21
  35. 51
  36. 4
  37. 5
  38. 7
  39. 4
  40. 19

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