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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 111 · 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.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 96 (c) 86 (d) 95
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  3. 3.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 316 (c) 306 (d) 315
  4. 4.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 216 (d) 217
  5. 5.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 198 (c) 66 (d) 22
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  7. 7.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) 14 (d) 42
  8. 8.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 387 (c) 336 (d) 396
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  10. 10.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 439 (d) 364
  11. 11.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) 24 (b) 72 (c) 8 (d) 27
  12. 12.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 406 (c) 396 (d) 342
  13. 13.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) 10 (b) 90 (c) 33 (d) 30
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 6 (b) 15 (c) 16 (d) 17
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  16. 16.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 99 (c) 90 (d) 100
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  18. 18.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 285 (c) 294 (d) 268
  19. 19.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 262 (c) 286 (d) 276
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 4 (d) 5
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 5 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 4 (b) 3 (c) 6 (d) 5
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 16 (b) 17 (c) 18 (d) 6
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 17 (d) 7
  29. 29.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) 42 (b) 39 (c) 117 (d) 13
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
  31. 31.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 480 (c) 603 (d) 612
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 4 (d) 3
  33. 33.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 64 (c) 74 (d) 73
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 5 (b) 4 (c) 7 (d) 6
  35. 35.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) 6 (c) 21 (d) 18
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 16 (d) 17
  37. 37.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) 153 (c) 17 (d) 51
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 8 (d) 19
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 6 (b) 8 (c) 10 (d) 11
  40. 40.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) 5 (b) 15 (c) 18 (d) 45

Answer key

  1. 95
  2. 7
  3. 315
  4. 216
  5. 66
  6. 5
  7. 42
  8. 396
  9. 8
  10. 438
  11. 24
  12. 405
  13. 30
  14. 16
  15. 3
  16. 99
  17. 8
  18. 294
  19. 285
  20. 4
  21. 3
  22. 4
  23. 4
  24. 6
  25. 5
  26. 5
  27. 17
  28. 18
  29. 39
  30. 17
  31. 612
  32. 4
  33. 73
  34. 6
  35. 18
  36. 17
  37. 51
  38. 19
  39. 10
  40. 15

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