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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 373 · 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 2 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 19 (d) 7
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 5 (d) 2
  3. 3.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
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  5. 5.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  6. 6.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 82 (c) 91 (d) 100
  7. 7.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) 144 (b) 16 (c) 51 (d) 48
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 10 (d) 3
  9. 9.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 125 (c) 116 (d) 134
  10. 10.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) 33 (b) 90 (c) 10 (d) 30
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 6 (b) 7 (c) 4 (d) 5
  13. 13.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) 54 (b) 21 (c) 18 (d) 6
  14. 14.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) 14 (b) 126 (c) 42 (d) 45
  15. 15.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) 24 (c) 21 (d) 7
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  18. 18.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
  19. 19.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) 164 (c) 163 (d) 154
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  21. 21.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 240 (c) 253 (d) 243
  22. 22.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 144 (d) 134
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 5 (d) 4
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 4 (b) 9 (c) 10 (d) 11
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 3 (d) 5
  26. 26.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 309 (c) 278 (d) 300
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  29. 29.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) 180 (b) 63 (c) 60 (d) 20
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 18 (d) 7
  31. 31.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) 330 (c) 331 (d) 292
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  33. 33.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) 48 (c) 45 (d) 135
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 13 (c) 14 (d) 15
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 16 (d) 6
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  39. 39.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 279 (d) 288
  40. 40.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) 13 (b) 117 (c) 42 (d) 39

Answer key

  1. 18
  2. 4
  3. 15
  4. 7
  5. 41
  6. 91
  7. 48
  8. 10
  9. 125
  10. 30
  11. 3
  12. 6
  13. 18
  14. 42
  15. 21
  16. 5
  17. 20
  18. 36
  19. 163
  20. 18
  21. 252
  22. 143
  23. 4
  24. 10
  25. 4
  26. 309
  27. 8
  28. 4
  29. 60
  30. 18
  31. 330
  32. 4
  33. 45
  34. 14
  35. 18
  36. 5
  37. 17
  38. 2
  39. 288
  40. 39

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