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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 522 · 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 4? (a) 4 (b) 10 (c) 3 (d) 5
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 4 (d) 5
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20
  4. 4.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 237 (c) 228 (d) 238
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 14 (c) 15 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  7. 7.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) 30 (b) 33 (c) 90 (d) 10
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  9. 9.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 62 (d) 70
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 18 (c) 7 (d) 17
  11. 11.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 534 (c) 434 (d) 543
  12. 12.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 114 (c) 132 (d) 123
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 7 (c) 9 (d) 8
  14. 14.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
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
  16. 16.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) 60 (b) 57 (c) 171 (d) 19
  17. 17.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 114 (d) 105
  18. 18.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) 18 (b) 21 (c) 54 (d) 6
  19. 19.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) 331 (c) 330 (d) 292
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 1 (b) 3 (c) 2 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 3 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  27. 27.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 540 (c) 432 (d) 531
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  29. 29.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) 7 (b) 21 (c) 63 (d) 24
  30. 30.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 228 (c) 225 (d) 235
  31. 31.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) 189 (b) 21 (c) 63 (d) 66
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 1
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  34. 34.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 112 (d) 111
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  36. 36.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) 361 (c) 312 (d) 360
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 3 (c) 14 (d) 13
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 5 (d) 16
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
  40. 40.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) 14 (c) 45 (d) 42

Answer key

  1. 4
  2. 5
  3. 19
  4. 237
  5. 15
  6. 9
  7. 30
  8. 20
  9. 61
  10. 18
  11. 543
  12. 123
  13. 8
  14. 45
  15. 3
  16. 57
  17. 105
  18. 18
  19. 330
  20. 8
  21. 2
  22. 18
  23. 3
  24. 7
  25. 4
  26. 9
  27. 540
  28. 3
  29. 21
  30. 234
  31. 63
  32. 3
  33. 19
  34. 111
  35. 8
  36. 360
  37. 14
  38. 16
  39. 18
  40. 42

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