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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 702 · 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 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 9 (d) 19
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 5 (d) 4
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
  7. 7.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 478 (c) 390 (d) 477
  8. 8.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  9. 9.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 88 (c) 70 (d) 80
  10. 10.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 35 (c) 44 (d) 26
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 13 (c) 4 (d) 14
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 13 (c) 3 (d) 14
  13. 13.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 306 (c) 297 (d) 276
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  15. 15.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 222 (c) 213 (d) 220
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  19. 19.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) 5 (b) 15 (c) 45 (d) 18
  20. 20.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
  21. 21.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) 21 (b) 24 (c) 63 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  23. 23.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
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 5 (b) 4 (c) 3 (d) 6
  25. 25.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
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  27. 27.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) 63 (c) 21 (d) 189
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 11 (b) 8 (c) 9 (d) 10
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 4 (d) 13
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 16 (b) 6 (c) 15 (d) 17
  31. 31.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) 24 (b) 75 (c) 72 (d) 216
  32. 32.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 500 (c) 643 (d) 642
  33. 33.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) 11 (b) 99 (c) 33 (d) 36
  34. 34.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 326 (c) 382 (d) 372
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 19 (d) 18
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 19 (d) 17
  37. 37.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 118 (c) 126 (d) 108
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  39. 39.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 555 (d) 546
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 9 (b) 6 (c) 5 (d) 8

Answer key

  1. 4
  2. 19
  3. 4
  4. 19
  5. 4
  6. 4
  7. 477
  8. 3
  9. 79
  10. 35
  11. 13
  12. 14
  13. 306
  14. 6
  15. 222
  16. 19
  17. 4
  18. 2
  19. 15
  20. 36
  21. 21
  22. 2
  23. 54
  24. 5
  25. 14
  26. 5
  27. 63
  28. 10
  29. 14
  30. 16
  31. 72
  32. 642
  33. 33
  34. 381
  35. 19
  36. 18
  37. 117
  38. 19
  39. 555
  40. 8

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