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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 311 · 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 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 235 (d) 234
  2. 2.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 636 (c) 496 (d) 627
  3. 3.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 537 (d) 546
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  6. 6.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) 99 (c) 33 (d) 36
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 20 (d) 21
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 16 (b) 17 (c) 6 (d) 18
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 13 (c) 4 (d) 15
  10. 10.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) 66 (c) 69 (d) 22
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  13. 13.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 64 (c) 46 (d) 55
  14. 14.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 624 (c) 488 (d) 615
  15. 15.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 400 (c) 483 (d) 493
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 6 (b) 7 (c) 5 (d) 4
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  20. 20.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 48 (d) 16
  21. 21.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 561 (c) 552 (d) 562
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 14 (c) 13 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 5 (b) 8 (c) 6 (d) 7
  25. 25.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) 14 (c) 45 (d) 42
  26. 26.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  27. 27.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) 39 (d) 13
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 5 (b) 16 (c) 17 (d) 15
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 12 (c) 14 (d) 13
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  31. 31.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 303 (c) 304 (d) 294
  32. 32.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) 30 (c) 27 (d) 9
  33. 33.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 106 (c) 116 (d) 115
  34. 34.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 60 (c) 50 (d) 68
  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) 30 (b) 33 (c) 90 (d) 10
  36. 36.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) 18 (b) 5 (c) 45 (d) 15
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  38. 38.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 394 (c) 334 (d) 384
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 18 (d) 17
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 7 (d) 17

Answer key

  1. 234
  2. 636
  3. 546
  4. 7
  5. 8
  6. 33
  7. 20
  8. 17
  9. 14
  10. 66
  11. 2
  12. 3
  13. 55
  14. 624
  15. 492
  16. 5
  17. 6
  18. 4
  19. 6
  20. 48
  21. 561
  22. 13
  23. 6
  24. 7
  25. 42
  26. 4
  27. 39
  28. 16
  29. 13
  30. 5
  31. 303
  32. 27
  33. 115
  34. 59
  35. 30
  36. 15
  37. 2
  38. 393
  39. 18
  40. 18

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