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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 45 · 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 3? (a) 4 (b) 2 (c) 3 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 19 (d) 18
  4. 4.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 58 (c) 40 (d) 49
  5. 5.The numbers 11 to 19 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) 48 (c) 135 (d) 15
  6. 6.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 355 (c) 354 (d) 345
  7. 7.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) 30 (b) 81 (c) 9 (d) 27
  8. 8.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) 153 (b) 51 (c) 54 (d) 17
  9. 9.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) 24 (b) 7 (c) 63 (d) 21
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 5 (d) 15
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 4 (d) 1
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 5 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
  15. 15.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 240 (c) 231 (d) 241
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 19 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  18. 18.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 119 (d) 110
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 17 (d) 6
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  21. 21.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) 54 (b) 21 (c) 18 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  23. 23.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 3 (b) 4 (c) 6 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 15 (b) 17 (c) 5 (d) 16
  28. 28.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 7 (b) 4 (c) 5 (d) 8
  30. 30.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) 48 (c) 51 (d) 16
  31. 31.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 151 (c) 160 (d) 152
  32. 32.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) 39 (c) 42 (d) 117
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 19 (d) 7
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 20 (d) 19
  35. 35.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 618 (c) 627 (d) 490
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 8 (b) 7 (c) 6 (d) 9
  38. 38.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 137 (d) 138
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 3 (d) 4
  40. 40.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) 198 (b) 69 (c) 22 (d) 66

Answer key

  1. 3
  2. 5
  3. 18
  4. 49
  5. 45
  6. 354
  7. 27
  8. 51
  9. 21
  10. 15
  11. 3
  12. 5
  13. 2
  14. 3
  15. 240
  16. 20
  17. 4
  18. 119
  19. 17
  20. 5
  21. 18
  22. 9
  23. 9
  24. 5
  25. 2
  26. 19
  27. 16
  28. 600
  29. 7
  30. 48
  31. 151
  32. 39
  33. 18
  34. 19
  35. 627
  36. 3
  37. 8
  38. 137
  39. 3
  40. 66

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