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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 17 · 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 13? (a) 7 (b) 5 (c) 6 (d) 14
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  3. 3.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 132 (c) 131 (d) 140
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  5. 5.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 444 (c) 453 (d) 454
  6. 6.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) 18 (c) 57 (d) 162
  7. 7.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) 54 (b) 51 (c) 17 (d) 153
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  11. 11.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) 171 (b) 19 (c) 57 (d) 60
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 7 (b) 6 (c) 5 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  14. 14.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 456 (c) 466 (d) 382
  15. 15.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 582 (c) 573 (d) 583
  16. 16.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 633 (c) 500 (d) 643
  17. 17.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 164 (c) 173 (d) 174
  18. 18.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 204 (c) 199 (d) 198
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 19 (d) 17
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  22. 22.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 186 (c) 202 (d) 196
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  24. 24.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 76 (d) 75
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 3 (d) 4
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 14 (d) 13
  27. 27.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 312 (c) 361 (d) 360
  28. 28.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 59 (d) 60
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 4 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 14 (c) 13 (d) 4
  32. 32.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) 36 (b) 11 (c) 33 (d) 99
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  35. 35.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 130 (c) 122 (d) 121
  36. 36.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 63 (c) 180 (d) 60
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
  38. 38.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
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 4 (d) 3

Answer key

  1. 6
  2. 8
  3. 131
  4. 4
  5. 453
  6. 54
  7. 51
  8. 19
  9. 5
  10. 7
  11. 57
  12. 6
  13. 3
  14. 465
  15. 582
  16. 642
  17. 173
  18. 198
  19. 18
  20. 9
  21. 18
  22. 195
  23. 6
  24. 75
  25. 5
  26. 14
  27. 360
  28. 59
  29. 5
  30. 3
  31. 14
  32. 33
  33. 3
  34. 7
  35. 121
  36. 60
  37. 14
  38. 15
  39. 4
  40. 4

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