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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 498 · 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) 8 (b) 10 (c) 6 (d) 7
  2. 2.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 309 (c) 278 (d) 310
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 18 (d) 6
  5. 5.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 160 (d) 159
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 5 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  9. 9.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) 15 (b) 135 (c) 48 (d) 45
  10. 10.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) 27 (c) 72 (d) 8
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 5 (b) 6 (c) 8 (d) 7
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 18 (d) 19
  13. 13.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 201 (c) 206 (d) 202
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 3 (d) 2
  16. 16.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 406 (c) 396 (d) 405
  17. 17.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) 66 (d) 22
  18. 18.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) 51 (b) 17 (c) 54 (d) 153
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  20. 20.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) 80 (c) 88 (d) 70
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  23. 23.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 45 (c) 42 (d) 14
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 4 (c) 3 (d) 2
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 15 (d) 14
  26. 26.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) 54 (b) 162 (c) 18 (d) 57
  27. 27.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) 5 (c) 45 (d) 15
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 13 (c) 3 (d) 14
  29. 29.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 225 (c) 222 (d) 226
  30. 30.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 361 (c) 360 (d) 351
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  32. 32.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 114 (d) 113
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 7 (c) 5 (d) 8
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  35. 35.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) 21 (b) 54 (c) 18 (d) 6
  36. 36.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 154 (c) 164 (d) 163
  37. 37.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 103 (c) 94 (d) 112
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 16 (d) 14
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 18 (d) 17

Answer key

  1. 7
  2. 309
  3. 3
  4. 17
  5. 159
  6. 4
  7. 2
  8. 9
  9. 45
  10. 24
  11. 7
  12. 19
  13. 201
  14. 5
  15. 4
  16. 405
  17. 66
  18. 51
  19. 19
  20. 79
  21. 9
  22. 3
  23. 42
  24. 3
  25. 14
  26. 54
  27. 15
  28. 13
  29. 225
  30. 360
  31. 4
  32. 113
  33. 7
  34. 8
  35. 18
  36. 163
  37. 103
  38. 15
  39. 20
  40. 17

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