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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 612 · 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.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 190 (c) 180 (d) 189
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  4. 4.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) 39 (d) 12
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 14 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  11. 11.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) 13 (b) 42 (c) 39 (d) 117
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 17 (d) 18
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 18 (d) 19
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 21 (d) 19
  15. 15.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 247 (c) 237 (d) 236
  16. 16.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
  17. 17.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
  18. 18.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) 579 (c) 570 (d) 580
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 4 (d) 3
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 6 (d) 3
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 17 (d) 8
  26. 26.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) 63 (b) 21 (c) 189 (d) 66
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 16 (b) 15 (c) 17 (d) 6
  29. 29.The numbers 4 to 12 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) 72 (c) 27 (d) 8
  30. 30.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 182 (c) 174 (d) 164
  31. 31.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 615 (c) 488 (d) 624
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 6 (b) 8 (c) 5 (d) 7
  33. 33.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 116 (c) 124 (d) 115
  34. 34.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 543 (d) 534
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 16 (d) 4
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 4 (d) 5
  38. 38.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) 18 (b) 57 (c) 162 (d) 54
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 13 (b) 12 (c) 11 (d) 5
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 3 (d) 14

Answer key

  1. 189
  2. 5
  3. 6
  4. 36
  5. 8
  6. 4
  7. 15
  8. 2
  9. 15
  10. 7
  11. 39
  12. 18
  13. 19
  14. 20
  15. 246
  16. 498
  17. 5
  18. 579
  19. 9
  20. 5
  21. 19
  22. 2
  23. 5
  24. 5
  25. 18
  26. 63
  27. 6
  28. 16
  29. 24
  30. 173
  31. 624
  32. 7
  33. 115
  34. 543
  35. 8
  36. 15
  37. 6
  38. 54
  39. 12
  40. 14

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