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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 512 · 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) 13 (b) 6 (c) 7 (d) 8
  2. 2.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) 63 (c) 21 (d) 189
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 5 (b) 15 (c) 14 (d) 16
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 15 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 9 (d) 20
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  9. 9.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 118 (c) 108 (d) 126
  10. 10.The numbers 5 to 13 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) 9 (c) 27 (d) 81
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 18 (b) 17 (c) 8 (d) 19
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 6 (d) 18
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 6 (b) 9 (c) 7 (d) 8
  14. 14.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) 11 (b) 36 (c) 33 (d) 99
  15. 15.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 570 (c) 580 (d) 458
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 16 (d) 17
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 5 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  20. 20.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 109 (d) 100
  21. 21.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 387 (c) 330 (d) 378
  22. 22.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 480 (d) 471
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 7 (c) 8 (d) 5
  25. 25.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) 18 (c) 21 (d) 6
  26. 26.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 183 (d) 192
  27. 27.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  28. 28.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 582 (d) 460
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  31. 31.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
  32. 32.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 52 (c) 44 (d) 34
  33. 33.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 376 (c) 322 (d) 366
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 10 (b) 8 (c) 5 (d) 11
  35. 35.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 172 (c) 162 (d) 180
  36. 36.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 397 (c) 387 (d) 396
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  38. 38.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) 57 (d) 18
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 7 (b) 5 (c) 8 (d) 6
  40. 40.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

Answer key

  1. 7
  2. 63
  3. 4
  4. 15
  5. 16
  6. 3
  7. 20
  8. 8
  9. 117
  10. 27
  11. 18
  12. 17
  13. 8
  14. 33
  15. 579
  16. 4
  17. 16
  18. 4
  19. 5
  20. 109
  21. 387
  22. 480
  23. 6
  24. 7
  25. 18
  26. 192
  27. 7
  28. 582
  29. 6
  30. 3
  31. 49
  32. 43
  33. 375
  34. 10
  35. 171
  36. 396
  37. 3
  38. 54
  39. 7
  40. 45

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