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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 636 · 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 62? (a) 10 (b) 6 (c) 7 (d) 9
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 15 (d) 4
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 13 (c) 15 (d) 4
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 19 (d) 18
  6. 6.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 309 (c) 319 (d) 318
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  8. 8.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 110 (c) 118 (d) 109
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 18 (d) 20
  10. 10.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) 75 (b) 24 (c) 72 (d) 216
  11. 11.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 302 (c) 336 (d) 345
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 8 (c) 15 (d) 13
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  15. 15.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 434 (c) 543 (d) 534
  16. 16.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 388 (c) 378 (d) 387
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  18. 18.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
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 14 (c) 3 (d) 15
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 15 (d) 5
  21. 21.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) 60 (c) 20 (d) 180
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 14 (d) 4
  23. 23.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) 60 (b) 171 (c) 57 (d) 19
  24. 24.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 90 (c) 98 (d) 80
  25. 25.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 181 (c) 190 (d) 172
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 5 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  29. 29.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 152 (d) 160
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 18 (d) 20
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 15 (d) 13
  35. 35.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 60 (c) 50 (d) 68
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  37. 37.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 76 (d) 66
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 4 (d) 15
  39. 39.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
  40. 40.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) 81 (d) 9

Answer key

  1. 9
  2. 3
  3. 15
  4. 14
  5. 18
  6. 318
  7. 19
  8. 109
  9. 19
  10. 72
  11. 345
  12. 6
  13. 15
  14. 3
  15. 543
  16. 387
  17. 9
  18. 15
  19. 14
  20. 15
  21. 60
  22. 15
  23. 57
  24. 89
  25. 181
  26. 7
  27. 2
  28. 4
  29. 151
  30. 19
  31. 4
  32. 9
  33. 5
  34. 14
  35. 59
  36. 4
  37. 75
  38. 15
  39. 48
  40. 27

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