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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 124 · 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 times is the digit 1 written when you write all the numbers from 1 to 39? (a) 3 (b) 13 (c) 15 (d) 14
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 3 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 13 (c) 3 (d) 15
  6. 6.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 316 (c) 367 (d) 366
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
  8. 8.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 106 (c) 88 (d) 97
  9. 9.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) 39 (b) 117 (c) 42 (d) 13
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 17 (c) 7 (d) 18
  11. 11.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 140 (c) 139 (d) 130
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 18 (d) 19
  14. 14.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) 9 (b) 81 (c) 27 (d) 30
  15. 15.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 162 (d) 171
  16. 16.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 39 (d) 12
  17. 17.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) 6 (b) 54 (c) 18 (d) 21
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  19. 19.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
  20. 20.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 85 (d) 76
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 7 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 15 (c) 16 (d) 6
  26. 26.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 211 (c) 201 (d) 210
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 9 (d) 19
  28. 28.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) 8 (b) 27 (c) 72 (d) 24
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  30. 30.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 216 (c) 72 (d) 24
  31. 31.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) 63 (b) 20 (c) 180 (d) 60
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 6 (b) 4 (c) 5 (d) 7
  33. 33.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) 21 (b) 7 (c) 63 (d) 24
  34. 34.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 38 (d) 47
  35. 35.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) 160 (c) 159 (d) 150
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 17 (b) 16 (c) 5 (d) 15
  37. 37.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 390 (d) 338
  38. 38.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  39. 39.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) 135 (b) 15 (c) 48 (d) 45
  40. 40.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) 60 (c) 57 (d) 19

Answer key

  1. 14
  2. 5
  3. 3
  4. 4
  5. 14
  6. 366
  7. 17
  8. 97
  9. 39
  10. 17
  11. 139
  12. 19
  13. 19
  14. 27
  15. 171
  16. 36
  17. 18
  18. 9
  19. 378
  20. 85
  21. 8
  22. 7
  23. 2
  24. 5
  25. 16
  26. 210
  27. 19
  28. 24
  29. 9
  30. 72
  31. 60
  32. 6
  33. 21
  34. 47
  35. 159
  36. 16
  37. 399
  38. 7
  39. 45
  40. 57

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