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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 980 · 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.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) 171 (c) 57 (d) 19
  2. 2.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) 45 (b) 126 (c) 42 (d) 14
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 1
  4. 4.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) 216 (b) 75 (c) 24 (d) 72
  5. 5.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 285 (c) 276 (d) 286
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  8. 8.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) 27 (b) 24 (c) 8 (d) 72
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  10. 10.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) 39 (b) 12 (c) 36 (d) 108
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  12. 12.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) 228 (c) 238 (d) 237
  13. 13.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 504 (d) 495
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  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) 21 (b) 7 (c) 24 (d) 63
  16. 16.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) 54 (c) 21 (d) 6
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 15 (d) 14
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 7 (d) 16
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 5 (d) 3
  22. 22.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 133 (c) 124 (d) 134
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 7 (d) 18
  24. 24.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 172 (d) 163
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  26. 26.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) 9 (c) 27 (d) 30
  27. 27.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 610 (c) 600 (d) 609
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 9 (d) 18
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 20 (d) 9
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 18 (d) 7
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 20 (d) 19
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 18 (b) 19 (c) 17 (d) 7
  34. 34.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 179 (c) 188 (d) 170
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 5 (b) 17 (c) 15 (d) 16
  36. 36.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 324 (c) 294 (d) 333
  37. 37.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 126 (d) 134
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  39. 39.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) 66 (b) 189 (c) 21 (d) 63
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 9 (c) 19 (d) 20

Answer key

  1. 57
  2. 42
  3. 3
  4. 72
  5. 285
  6. 33
  7. 8
  8. 24
  9. 2
  10. 36
  11. 20
  12. 237
  13. 504
  14. 4
  15. 21
  16. 18
  17. 14
  18. 17
  19. 18
  20. 6
  21. 5
  22. 133
  23. 18
  24. 163
  25. 7
  26. 27
  27. 609
  28. 4
  29. 19
  30. 20
  31. 18
  32. 20
  33. 18
  34. 179
  35. 16
  36. 333
  37. 125
  38. 3
  39. 63
  40. 20

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