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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 318 · 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 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) 108 (b) 12 (c) 39 (d) 36
  2. 2.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 158 (c) 150 (d) 149
  3. 3.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 134 (d) 126
  4. 4.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 96 (d) 105
  5. 5.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) 81 (b) 9 (c) 30 (d) 27
  6. 6.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) 39 (c) 42 (d) 13
  7. 7.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) 18 (c) 5 (d) 15
  8. 8.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) 54 (c) 6 (d) 18
  9. 9.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 339 (c) 340 (d) 298
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 18 (d) 16
  13. 13.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 216 (c) 225 (d) 226
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 5 (c) 6 (d) 7
  15. 15.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) 69 (c) 198 (d) 22
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  17. 17.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 482 (d) 615
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 7 (c) 9 (d) 8
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 16 (d) 17
  21. 21.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) 19 (b) 171 (c) 57 (d) 60
  22. 22.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 570 (c) 561 (d) 452
  23. 23.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) 36 (b) 33 (c) 11 (d) 99
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 13 (c) 5 (d) 12
  26. 26.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 19 (d) 8
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 7 (b) 5 (c) 4 (d) 6
  30. 30.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 298 (c) 288 (d) 297
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 10 (d) 11
  32. 32.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) 411 (d) 402
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 12 (c) 3 (d) 13
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 6 (b) 14 (c) 16 (d) 15
  35. 35.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) 33 (c) 30 (d) 10
  36. 36.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 362 (d) 436
  37. 37.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 84 (c) 102 (d) 93
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 8 (b) 17 (c) 18 (d) 19
  39. 39.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 406 (c) 501 (d) 492
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 18 (d) 17

Answer key

  1. 36
  2. 149
  3. 125
  4. 105
  5. 27
  6. 39
  7. 15
  8. 18
  9. 339
  10. 6
  11. 8
  12. 17
  13. 225
  14. 7
  15. 66
  16. 3
  17. 615
  18. 8
  19. 5
  20. 16
  21. 57
  22. 570
  23. 33
  24. 2
  25. 12
  26. 4
  27. 4
  28. 19
  29. 6
  30. 297
  31. 11
  32. 411
  33. 13
  34. 15
  35. 30
  36. 435
  37. 93
  38. 18
  39. 501
  40. 17

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