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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 230 · 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 times is the digit 1 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 16 (d) 17
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 13 (c) 12 (d) 3
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 18 (d) 17
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 19 (d) 20
  7. 7.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) 39 (b) 13 (c) 117 (d) 42
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 1 (d) 4
  9. 9.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
  10. 10.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 78 (d) 60
  11. 11.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 579 (d) 570
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  14. 14.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) 23 (c) 72 (d) 69
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 14 (d) 15
  17. 17.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 22 (c) 66 (d) 69
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 19 (d) 8
  19. 19.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) 14 (b) 126 (c) 42 (d) 45
  20. 20.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 139 (d) 148
  21. 21.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 172 (d) 163
  22. 22.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) 9 (b) 30 (c) 27 (d) 81
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  24. 24.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 414 (c) 514 (d) 504
  25. 25.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) 153 (b) 54 (c) 17 (d) 51
  26. 26.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 60 (d) 180
  27. 27.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) 144 (b) 51 (c) 16 (d) 48
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 5 (d) 3
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 16 (d) 17
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 4 (b) 6 (c) 5 (d) 7
  31. 31.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 153 (c) 144 (d) 162
  32. 32.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 558 (c) 450 (d) 567
  33. 33.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 125 (d) 134
  34. 34.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) 36 (b) 99 (c) 33 (d) 11
  35. 35.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 192 (c) 206 (d) 201
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 10 (b) 4 (c) 11 (d) 12
  37. 37.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 588 (d) 597
  38. 38.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) 297 (c) 276 (d) 307
  39. 39.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 58 (c) 49 (d) 40
  40. 40.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 411 (c) 420 (d) 352

Answer key

  1. 17
  2. 12
  3. 17
  4. 4
  5. 17
  6. 19
  7. 39
  8. 3
  9. 57
  10. 69
  11. 579
  12. 4
  13. 7
  14. 69
  15. 18
  16. 15
  17. 66
  18. 19
  19. 42
  20. 139
  21. 163
  22. 27
  23. 6
  24. 513
  25. 51
  26. 60
  27. 48
  28. 4
  29. 17
  30. 6
  31. 153
  32. 567
  33. 125
  34. 33
  35. 201
  36. 11
  37. 597
  38. 306
  39. 49
  40. 420

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