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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 407 · 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.

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  1. 1.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 100 (c) 118 (d) 109
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 3 (d) 4
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 17 (d) 16
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 15 (d) 5
  5. 5.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 433 (c) 360 (d) 423
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  7. 7.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
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 17 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  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) 10 (b) 30 (c) 90 (d) 33
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 4 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 19 (d) 20
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  15. 15.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) 27 (b) 81 (c) 30 (d) 9
  16. 16.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 114 (c) 113 (d) 104
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  18. 18.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 508 (c) 410 (d) 507
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 7 (c) 12 (d) 13
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 3 (d) 13
  21. 21.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) 153 (b) 17 (c) 51 (d) 54
  22. 22.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 249 (d) 238
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 1
  24. 24.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) 20 (c) 63 (d) 60
  25. 25.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) 198 (b) 69 (c) 66 (d) 22
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 17
  27. 27.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) 33 (b) 99 (c) 36 (d) 11
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 18 (d) 6
  29. 29.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) 24 (c) 27 (d) 72
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  31. 31.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 366 (c) 441 (d) 442
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 19 (b) 20 (c) 8 (d) 18
  33. 33.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 276 (c) 277 (d) 267
  34. 34.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) 63 (c) 24 (d) 7
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 15 (d) 16
  36. 36.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) 16 (b) 144 (c) 48 (d) 51
  37. 37.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 387 (c) 336 (d) 397
  38. 38.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) 279 (c) 288 (d) 289
  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) 15 (b) 45 (c) 48 (d) 135
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20

Answer key

  1. 109
  2. 3
  3. 16
  4. 16
  5. 432
  6. 8
  7. 378
  8. 18
  9. 3
  10. 30
  11. 15
  12. 3
  13. 19
  14. 8
  15. 27
  16. 113
  17. 19
  18. 507
  19. 12
  20. 14
  21. 51
  22. 249
  23. 3
  24. 60
  25. 66
  26. 18
  27. 33
  28. 17
  29. 24
  30. 9
  31. 441
  32. 19
  33. 276
  34. 21
  35. 15
  36. 48
  37. 396
  38. 288
  39. 45
  40. 20

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