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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 143 · 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 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
  2. 2.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 98 (c) 88 (d) 106
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  4. 4.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 624 (d) 625
  5. 5.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) 16 (c) 51 (d) 48
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 5 (d) 2
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  10. 10.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) 48 (b) 15 (c) 45 (d) 135
  11. 11.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 426 (c) 356 (d) 417
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 17 (c) 6 (d) 16
  13. 13.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) 20 (b) 60 (c) 180 (d) 63
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 12 (c) 13 (d) 3
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 18 (d) 19
  17. 17.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 394 (c) 484 (d) 483
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 13 (c) 14 (d) 3
  19. 19.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 128 (c) 136 (d) 127
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 8 (d) 5
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 558 (c) 568 (d) 450
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 14 (c) 4 (d) 12
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 17 (d) 16
  27. 27.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) 51 (d) 17
  28. 28.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) 10 (b) 30 (c) 90 (d) 33
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  30. 30.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 465 (d) 456
  31. 31.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 76 (c) 85 (d) 86
  32. 32.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 184 (c) 166 (d) 175
  33. 33.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 294 (c) 295 (d) 268
  34. 34.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 414 (c) 423 (d) 424
  35. 35.The numbers 17 to 25 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) 189 (c) 63 (d) 66
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 20
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  38. 38.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) 8 (b) 27 (c) 72 (d) 24
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4

Answer key

  1. 243
  2. 97
  3. 5
  4. 624
  5. 48
  6. 4
  7. 20
  8. 2
  9. 9
  10. 45
  11. 426
  12. 17
  13. 60
  14. 4
  15. 13
  16. 19
  17. 483
  18. 13
  19. 127
  20. 7
  21. 4
  22. 567
  23. 7
  24. 13
  25. 6
  26. 17
  27. 51
  28. 30
  29. 6
  30. 465
  31. 85
  32. 175
  33. 294
  34. 423
  35. 63
  36. 19
  37. 18
  38. 24
  39. 8
  40. 4

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