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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 642 · 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.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) 39 (c) 36 (d) 12
  2. 2.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 202 (d) 201
  3. 3.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 369 (c) 318 (d) 370
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  5. 5.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 280 (c) 313 (d) 312
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 7 (b) 6 (c) 5 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  9. 9.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 297 (d) 276
  10. 10.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) 207 (b) 69 (c) 72 (d) 23
  11. 11.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) 15 (b) 48 (c) 135 (d) 45
  12. 12.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) 16 (b) 51 (c) 48 (d) 144
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 2 (c) 3 (d) 4
  14. 14.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 52 (d) 60
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 16 (d) 6
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 9 (d) 19
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 7 (c) 8 (d) 6
  18. 18.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
  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) 127 (b) 128 (c) 136 (d) 118
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 5 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  23. 23.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 463 (c) 453 (d) 380
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 9 (b) 14 (c) 11 (d) 13
  26. 26.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 96 (d) 95
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 3 (d) 5
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 20 (d) 18
  31. 31.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) 66 (d) 63
  32. 32.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) 54 (b) 57 (c) 162 (d) 18
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 4 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  35. 35.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 28 (c) 37 (d) 46
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 4 (d) 5
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 1 (c) 2 (d) 3
  38. 38.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 498 (c) 404 (d) 489
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 3 (d) 2
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4

Answer key

  1. 36
  2. 201
  3. 369
  4. 9
  5. 312
  6. 7
  7. 4
  8. 9
  9. 306
  10. 69
  11. 45
  12. 48
  13. 4
  14. 51
  15. 17
  16. 19
  17. 7
  18. 33
  19. 127
  20. 6
  21. 4
  22. 6
  23. 462
  24. 3
  25. 13
  26. 95
  27. 2
  28. 8
  29. 5
  30. 19
  31. 63
  32. 54
  33. 4
  34. 8
  35. 37
  36. 4
  37. 3
  38. 498
  39. 3
  40. 4

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