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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 908 · 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.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  2. 2.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) 42 (b) 126 (c) 14 (d) 45
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 9 (b) 12 (c) 11 (d) 7
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  5. 5.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 267 (c) 258 (d) 268
  6. 6.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
  7. 7.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) 10 (c) 33 (d) 90
  8. 8.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 448 (c) 447 (d) 370
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 2 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  12. 12.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 343 (c) 342 (d) 333
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  14. 14.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 92 (c) 91 (d) 82
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 4 (b) 2 (c) 3 (d) 5
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 6 (c) 4 (d) 5
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 7 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  21. 21.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 480 (c) 603 (d) 612
  22. 22.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 298 (c) 330 (d) 339
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 19 (d) 20
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  26. 26.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 137 (c) 138 (d) 146
  27. 27.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 36 (c) 35 (d) 44
  28. 28.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) 295 (c) 294 (d) 268
  29. 29.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) 99 (b) 11 (c) 33 (d) 36
  30. 30.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) 24 (b) 63 (c) 21 (d) 7
  31. 31.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 207 (c) 324 (d) 217
  32. 32.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 76 (d) 85
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 20 (d) 8
  34. 34.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) 189 (b) 63 (c) 66 (d) 21
  35. 35.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 62 (c) 72 (d) 80
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 21 (d) 9
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 9 (b) 8 (c) 7 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5

Answer key

  1. 6
  2. 42
  3. 11
  4. 5
  5. 267
  6. 432
  7. 30
  8. 447
  9. 4
  10. 4
  11. 3
  12. 342
  13. 8
  14. 91
  15. 2
  16. 4
  17. 5
  18. 6
  19. 9
  20. 7
  21. 612
  22. 339
  23. 19
  24. 9
  25. 2
  26. 137
  27. 35
  28. 294
  29. 33
  30. 21
  31. 216
  32. 85
  33. 19
  34. 63
  35. 71
  36. 20
  37. 19
  38. 8
  39. 8
  40. 4

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