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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 123 · 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 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) 17 (c) 51 (d) 153
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 18 (b) 19 (c) 7 (d) 17
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 6 (c) 5 (d) 7
  4. 4.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
  5. 5.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 23 (d) 69
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  7. 7.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 125 (c) 126 (d) 116
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  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) 13 (c) 117 (d) 42
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 5 (c) 3 (d) 4
  11. 11.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) 42 (c) 126 (d) 45
  12. 12.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 237 (c) 246 (d) 247
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 6 (b) 9 (c) 8 (d) 7
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 3 (c) 12 (d) 14
  15. 15.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 178 (c) 186 (d) 177
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  18. 18.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) 48 (b) 144 (c) 16 (d) 51
  19. 19.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 271 (d) 270
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  21. 21.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 39 (c) 48 (d) 30
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  26. 26.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 118 (c) 126 (d) 117
  27. 27.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 502 (c) 501 (d) 492
  28. 28.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 301 (c) 300 (d) 291
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 9 (d) 18
  30. 30.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 78 (c) 69 (d) 60
  31. 31.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  32. 32.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
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 7 (c) 8 (d) 5
  34. 34.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 399 (c) 409 (d) 408
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 2 (b) 5 (c) 3 (d) 4
  37. 37.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 466 (c) 592 (d) 591
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 15 (d) 14
  39. 39.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 290 (c) 327 (d) 318
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2

Answer key

  1. 51
  2. 18
  3. 6
  4. 57
  5. 69
  6. 2
  7. 125
  8. 2
  9. 39
  10. 4
  11. 42
  12. 246
  13. 8
  14. 13
  15. 177
  16. 5
  17. 4
  18. 48
  19. 270
  20. 7
  21. 39
  22. 4
  23. 5
  24. 7
  25. 9
  26. 117
  27. 501
  28. 300
  29. 19
  30. 69
  31. 3
  32. 63
  33. 7
  34. 408
  35. 16
  36. 4
  37. 591
  38. 14
  39. 327
  40. 4

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