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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 480 · 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 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 619 (c) 609 (d) 484
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 15 (d) 16
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 15 (d) 14
  5. 5.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 168 (c) 167 (d) 158
  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) 27 (b) 72 (c) 24 (d) 8
  7. 7.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 393 (c) 384 (d) 334
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 5 (b) 6 (c) 4 (d) 3
  9. 9.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 172 (c) 154 (d) 164
  10. 10.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
  11. 11.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 267 (c) 276 (d) 256
  12. 12.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 57 (d) 60
  13. 13.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 351 (c) 352 (d) 306
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  15. 15.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) 207 (d) 23
  16. 16.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 18 (c) 54 (d) 57
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 16 (b) 7 (c) 15 (d) 17
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 18 (d) 20
  20. 20.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
  21. 21.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) 15 (b) 45 (c) 5 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  25. 25.The numbers 2 to 10 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) 18 (c) 6 (d) 21
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  27. 27.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 382 (c) 466 (d) 465
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 4 (d) 2
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 15 (c) 13 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 4 (d) 16
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  33. 33.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
  34. 34.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 202 (c) 206 (d) 192
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 4 (d) 5
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 13 (b) 9 (c) 12 (d) 10
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 13 (b) 14 (c) 3 (d) 15
  38. 38.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 270 (d) 279
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 4 (d) 5
  40. 40.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) 33 (b) 90 (c) 30 (d) 10

Answer key

  1. 618
  2. 15
  3. 5
  4. 15
  5. 167
  6. 24
  7. 393
  8. 5
  9. 163
  10. 33
  11. 276
  12. 57
  13. 351
  14. 19
  15. 69
  16. 54
  17. 3
  18. 16
  19. 19
  20. 51
  21. 15
  22. 4
  23. 9
  24. 6
  25. 18
  26. 9
  27. 465
  28. 4
  29. 14
  30. 5
  31. 15
  32. 6
  33. 175
  34. 201
  35. 6
  36. 12
  37. 14
  38. 279
  39. 5
  40. 30

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