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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 383 · 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 8 written when you write all the numbers from 1 to 79? (a) 9 (b) 7 (c) 6 (d) 8
  2. 2.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) 33 (c) 99 (d) 11
  3. 3.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 14 (b) 16 (c) 4 (d) 15
  6. 6.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
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 5 (c) 4 (d) 3
  8. 8.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 442 (c) 556 (d) 555
  9. 9.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 222 (c) 225 (d) 226
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 19 (c) 20 (d) 9
  11. 11.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 598 (c) 588 (d) 597
  12. 12.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) 18 (b) 21 (c) 54 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 8 (b) 5 (c) 6 (d) 7
  15. 15.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) 45 (b) 18 (c) 5 (d) 15
  16. 16.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) 57 (c) 171 (d) 60
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  19. 19.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 177 (c) 168 (d) 186
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  21. 21.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) 27 (b) 30 (c) 9 (d) 81
  22. 22.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 217 (c) 207 (d) 216
  23. 23.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 110 (c) 119 (d) 128
  24. 24.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) 153 (c) 17 (d) 51
  25. 25.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 285 (d) 262
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 9 (d) 21
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 14 (d) 13
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 11 (b) 8 (c) 9 (d) 12
  30. 30.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 452 (c) 561 (d) 571
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 3 (d) 6
  32. 32.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 591 (c) 592 (d) 582
  33. 33.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 423 (c) 414 (d) 424
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 4 (d) 13
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 7 (b) 9 (c) 8 (d) 6
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 16 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  38. 38.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) 66 (b) 198 (c) 69 (d) 22
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5

Answer key

  1. 8
  2. 33
  3. 7
  4. 3
  5. 15
  6. 294
  7. 5
  8. 555
  9. 225
  10. 20
  11. 597
  12. 18
  13. 2
  14. 7
  15. 15
  16. 57
  17. 5
  18. 8
  19. 177
  20. 4
  21. 27
  22. 216
  23. 119
  24. 51
  25. 285
  26. 3
  27. 20
  28. 14
  29. 11
  30. 570
  31. 5
  32. 591
  33. 423
  34. 14
  35. 8
  36. 16
  37. 2
  38. 66
  39. 4
  40. 4

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