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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 307 · 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 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 292 (c) 330 (d) 331
  2. 2.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) 17 (c) 51 (d) 54
  3. 3.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) 81 (b) 30 (c) 27 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 3 (d) 5
  7. 7.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) 63 (b) 21 (c) 7 (d) 24
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 3 (b) 5 (c) 2 (d) 4
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 4 (c) 3 (d) 6
  10. 10.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 122 (d) 104
  11. 11.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 52 (d) 61
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  13. 13.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) 144 (d) 48
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 3 (d) 4
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 4 (d) 7
  17. 17.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 99 (c) 33 (d) 36
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 9 (b) 20 (c) 18 (d) 19
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
  21. 21.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 451 (d) 450
  22. 22.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 186 (c) 185 (d) 194
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  24. 24.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 69 (c) 23 (d) 207
  25. 25.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 627 (c) 628 (d) 490
  26. 26.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) 57 (b) 171 (c) 60 (d) 19
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 13 (d) 14
  28. 28.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 182 (c) 172 (d) 181
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 7 (d) 5
  30. 30.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 280 (d) 303
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 17 (d) 16
  34. 34.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) 66 (c) 21 (d) 189
  35. 35.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) 42 (b) 13 (c) 117 (d) 39
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 18 (d) 20
  37. 37.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 136 (c) 154 (d) 146
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  39. 39.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 356 (d) 426
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2

Answer key

  1. 330
  2. 51
  3. 27
  4. 6
  5. 6
  6. 5
  7. 21
  8. 4
  9. 6
  10. 113
  11. 61
  12. 7
  13. 48
  14. 3
  15. 4
  16. 6
  17. 33
  18. 9
  19. 19
  20. 18
  21. 450
  22. 185
  23. 5
  24. 69
  25. 627
  26. 57
  27. 14
  28. 181
  29. 6
  30. 312
  31. 5
  32. 2
  33. 16
  34. 63
  35. 39
  36. 19
  37. 145
  38. 20
  39. 426
  40. 2

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