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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 377 · 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) 19 (b) 18 (c) 9 (d) 20
  2. 2.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 348 (c) 415 (d) 405
  3. 3.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 130 (c) 138 (d) 129
  4. 4.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  5. 5.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) 54 (b) 51 (c) 17 (d) 153
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 5 (d) 3
  7. 7.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 500 (c) 633 (d) 643
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 20 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  12. 12.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 149 (d) 140
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 16 (b) 17 (c) 18 (d) 7
  17. 17.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 195 (c) 196 (d) 202
  18. 18.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) 9 (b) 30 (c) 81 (d) 27
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 14 (b) 13 (c) 15 (d) 3
  20. 20.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) 60 (b) 171 (c) 19 (d) 57
  21. 21.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) 24 (b) 7 (c) 63 (d) 21
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 15 (c) 16 (d) 14
  23. 23.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
  24. 24.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) 180 (d) 60
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 8 (d) 19
  26. 26.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) 27 (b) 8 (c) 24 (d) 72
  27. 27.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 346 (c) 402 (d) 411
  28. 28.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) 69 (b) 72 (c) 23 (d) 207
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 6 (d) 5
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  33. 33.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 409 (c) 408 (d) 399
  34. 34.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 469 (c) 459 (d) 384
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  36. 36.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
  37. 37.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) 18 (b) 54 (c) 6 (d) 21
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  40. 40.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 325 (c) 288 (d) 324

Answer key

  1. 19
  2. 414
  3. 129
  4. 3
  5. 51
  6. 5
  7. 642
  8. 8
  9. 20
  10. 7
  11. 19
  12. 149
  13. 6
  14. 5
  15. 2
  16. 17
  17. 195
  18. 27
  19. 14
  20. 57
  21. 21
  22. 15
  23. 72
  24. 60
  25. 19
  26. 24
  27. 411
  28. 69
  29. 9
  30. 7
  31. 6
  32. 4
  33. 408
  34. 468
  35. 4
  36. 30
  37. 18
  38. 3
  39. 16
  40. 324

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