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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 168 · 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 two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  3. 3.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 212 (c) 210 (d) 201
  4. 4.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 558 (d) 568
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 4 (d) 3
  9. 9.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
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 20
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  12. 12.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 328 (c) 318 (d) 327
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 13 (c) 15 (d) 3
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 8 (d) 20
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 16 (b) 18 (c) 9 (d) 19
  16. 16.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 241 (c) 240 (d) 232
  17. 17.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 74 (c) 84 (d) 83
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 13 (b) 6 (c) 10 (d) 12
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 16
  21. 21.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) 18 (b) 15 (c) 45 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 6 (d) 3
  24. 24.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 30 (d) 90
  25. 25.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 155 (c) 164 (d) 156
  26. 26.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) 8 (b) 27 (c) 72 (d) 24
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  30. 30.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) 189 (c) 63 (d) 21
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 18 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 8 (c) 7 (d) 6
  34. 34.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) 16 (b) 51 (c) 48 (d) 144
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 9 (d) 6
  36. 36.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 130 (c) 121 (d) 112
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 4 (d) 5
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 2 (d) 4
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 3 (c) 13 (d) 14

Answer key

  1. 7
  2. 5
  3. 210
  4. 567
  5. 4
  6. 2
  7. 5
  8. 5
  9. 345
  10. 19
  11. 9
  12. 327
  13. 14
  14. 19
  15. 18
  16. 240
  17. 83
  18. 4
  19. 12
  20. 17
  21. 15
  22. 6
  23. 5
  24. 30
  25. 155
  26. 24
  27. 15
  28. 19
  29. 2
  30. 63
  31. 18
  32. 6
  33. 8
  34. 48
  35. 8
  36. 121
  37. 4
  38. 4
  39. 3
  40. 14

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