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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 221 · 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 16? (a) 3 (b) 17 (c) 2 (d) 4
  2. 2.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) 13 (b) 39 (c) 117 (d) 42
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 7 (b) 5 (c) 4 (d) 6
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 21 (d) 9
  6. 6.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) 24 (b) 27 (c) 72 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  9. 9.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) 21 (c) 63 (d) 24
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 14 (c) 16 (d) 4
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 15 (b) 5 (c) 16 (d) 17
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 18 (c) 16 (d) 17
  13. 13.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) 72 (c) 24 (d) 216
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  15. 15.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 369 (c) 379 (d) 378
  16. 16.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 226 (d) 222
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 3 (c) 6 (d) 5
  19. 19.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 118 (c) 109 (d) 110
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  21. 21.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 331 (c) 330 (d) 292
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 13 (d) 15
  25. 25.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) 108 (b) 36 (c) 12 (d) 39
  26. 26.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 173 (c) 182 (d) 174
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 13 (c) 14 (d) 11
  28. 28.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) 9 (c) 27 (d) 81
  29. 29.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 417 (c) 350 (d) 408
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  31. 31.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 201 (c) 202 (d) 192
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 15 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 5 (b) 3 (c) 6 (d) 4
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 6 (b) 4 (c) 5 (d) 7
  36. 36.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 579 (c) 589 (d) 588
  37. 37.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) 17 (c) 153 (d) 51
  38. 38.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 133 (c) 124 (d) 142
  39. 39.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) 21 (c) 189 (d) 63
  40. 40.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 38 (c) 47 (d) 56

Answer key

  1. 3
  2. 39
  3. 6
  4. 20
  5. 20
  6. 24
  7. 8
  8. 7
  9. 21
  10. 15
  11. 16
  12. 17
  13. 72
  14. 4
  15. 378
  16. 231
  17. 6
  18. 5
  19. 109
  20. 2
  21. 330
  22. 5
  23. 3
  24. 14
  25. 36
  26. 173
  27. 13
  28. 27
  29. 417
  30. 6
  31. 201
  32. 14
  33. 9
  34. 5
  35. 6
  36. 588
  37. 51
  38. 133
  39. 63
  40. 47

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