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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 735 · 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.The numbers 18 to 26 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) 22 (c) 69 (d) 198
  2. 2.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) 45 (d) 48
  3. 3.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 621 (c) 612 (d) 486
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  5. 5.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) 6 (b) 54 (c) 18 (d) 21
  6. 6.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 285 (d) 262
  7. 7.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 405 (c) 348 (d) 414
  8. 8.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) 27 (b) 9 (c) 81 (d) 30
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  10. 10.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 178 (c) 160 (d) 169
  11. 11.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) 180 (b) 60 (c) 20 (d) 63
  12. 12.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) 21 (c) 7 (d) 63
  13. 13.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
  14. 14.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) 153 (c) 17 (d) 51
  15. 15.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 226 (c) 225 (d) 222
  16. 16.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 136 (c) 145 (d) 154
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 8 (b) 6 (c) 7 (d) 9
  18. 18.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) 216 (b) 75 (c) 24 (d) 72
  19. 19.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
  20. 20.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 429 (c) 430 (d) 420
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  22. 22.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 76 (c) 75 (d) 84
  23. 23.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) 30 (b) 90 (c) 33 (d) 10
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 3 (d) 1
  25. 25.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) 12 (b) 39 (c) 36 (d) 108
  26. 26.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 334 (c) 324 (d) 294
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 5 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  29. 29.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 70 (c) 88 (d) 79
  30. 30.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
  31. 31.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 128 (c) 118 (d) 136
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 20 (b) 8 (c) 18 (d) 19
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
  34. 34.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 279 (d) 270
  35. 35.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 14 (d) 16
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 19 (d) 21
  38. 38.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 510 (c) 412 (d) 501
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 17 (d) 18
  40. 40.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 58 (c) 49 (d) 50

Answer key

  1. 66
  2. 45
  3. 621
  4. 7
  5. 18
  6. 285
  7. 414
  8. 27
  9. 7
  10. 169
  11. 60
  12. 21
  13. 17
  14. 51
  15. 225
  16. 145
  17. 8
  18. 72
  19. 54
  20. 429
  21. 3
  22. 75
  23. 30
  24. 3
  25. 36
  26. 333
  27. 5
  28. 4
  29. 79
  30. 642
  31. 127
  32. 19
  33. 20
  34. 279
  35. 6
  36. 15
  37. 20
  38. 510
  39. 17
  40. 49

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