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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 422 · 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 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 460 (c) 573 (d) 583
  2. 2.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 150 (c) 142 (d) 132
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 20 (d) 21
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 7 (b) 8 (c) 6 (d) 5
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
  7. 7.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 531 (c) 532 (d) 426
  8. 8.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 523 (c) 513 (d) 420
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  10. 10.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) 51 (b) 17 (c) 153 (d) 54
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  12. 12.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) 75 (b) 24 (c) 216 (d) 72
  13. 13.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) 615 (c) 624 (d) 488
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 9 (b) 10 (c) 7 (d) 8
  16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 274 (d) 294
  17. 17.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) 72 (b) 69 (c) 23 (d) 207
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  19. 19.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 175 (c) 184 (d) 176
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 19 (d) 8
  21. 21.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) 66 (b) 63 (c) 21 (d) 189
  22. 22.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 450 (c) 459 (d) 378
  23. 23.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 310 (c) 278 (d) 300
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 9 (d) 20
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 7 (d) 19
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 19 (d) 18
  27. 27.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 118 (c) 109 (d) 100
  28. 28.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 5 (b) 8 (c) 9 (d) 6
  30. 30.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 331 (c) 321 (d) 330
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  32. 32.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 140 (c) 139 (d) 130
  33. 33.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) 30 (b) 81 (c) 9 (d) 27
  34. 34.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) 45 (b) 135 (c) 15 (d) 48
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 2 (d) 3
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 16 (b) 6 (c) 17 (d) 15
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 5 (d) 16
  39. 39.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) 108 (c) 36 (d) 39
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8

Answer key

  1. 582
  2. 141
  3. 3
  4. 20
  5. 7
  6. 19
  7. 531
  8. 522
  9. 4
  10. 51
  11. 5
  12. 72
  13. 624
  14. 7
  15. 9
  16. 303
  17. 69
  18. 2
  19. 175
  20. 19
  21. 63
  22. 459
  23. 309
  24. 19
  25. 18
  26. 19
  27. 109
  28. 7
  29. 8
  30. 330
  31. 6
  32. 139
  33. 27
  34. 45
  35. 4
  36. 16
  37. 6
  38. 16
  39. 36
  40. 9

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