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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 683 · 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.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 412 (c) 411 (d) 402
  2. 2.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 148 (c) 147 (d) 138
  3. 3.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) 171 (b) 19 (c) 60 (d) 57
  4. 4.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 406 (c) 405 (d) 342
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  6. 6.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) 60 (b) 63 (c) 180 (d) 20
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 19 (d) 17
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 6 (b) 4 (c) 7 (d) 5
  10. 10.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 543 (c) 544 (d) 434
  11. 11.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 478 (d) 477
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 12 (b) 9 (c) 14 (d) 15
  15. 15.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 282 (d) 260
  16. 16.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) 126 (b) 42 (c) 14 (d) 45
  17. 17.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 496 (c) 637 (d) 636
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 15 (c) 14 (d) 3
  19. 19.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) 42 (c) 13 (d) 39
  20. 20.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 531 (c) 432 (d) 540
  21. 21.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 504 (c) 408 (d) 505
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 5 (c) 7 (d) 10
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 5 (b) 4 (c) 6 (d) 7
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  25. 25.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) 7 (b) 24 (c) 21 (d) 63
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 7 (c) 6 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 11 (c) 12 (d) 10
  29. 29.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) 198 (b) 22 (c) 69 (d) 66
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 15 (b) 5 (c) 16 (d) 17
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  34. 34.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) 72 (c) 23 (d) 69
  35. 35.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
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 3 (b) 5 (c) 4 (d) 2
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  38. 38.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) 135 (b) 48 (c) 15 (d) 45
  39. 39.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 234 (c) 351 (d) 243
  40. 40.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) 216 (c) 75 (d) 72

Answer key

  1. 411
  2. 147
  3. 57
  4. 405
  5. 9
  6. 60
  7. 8
  8. 18
  9. 6
  10. 543
  11. 477
  12. 3
  13. 4
  14. 14
  15. 282
  16. 42
  17. 636
  18. 14
  19. 39
  20. 540
  21. 504
  22. 9
  23. 6
  24. 5
  25. 21
  26. 6
  27. 3
  28. 11
  29. 66
  30. 16
  31. 6
  32. 4
  33. 3
  34. 69
  35. 54
  36. 4
  37. 8
  38. 45
  39. 243
  40. 72

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