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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 756 · 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 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 145 (c) 136 (d) 146
  2. 2.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) 17 (b) 153 (c) 54 (d) 51
  3. 3.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 255 (c) 264 (d) 248
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 17 (c) 16 (d) 15
  5. 5.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 229 (d) 228
  6. 6.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 190 (c) 189 (d) 198
  7. 7.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 391 (d) 332
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 18 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 3 (c) 7 (d) 4
  13. 13.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 507 (c) 498 (d) 410
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 20 (d) 19
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 18
  16. 16.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) 36 (b) 33 (c) 99 (d) 11
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  19. 19.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 52 (c) 34 (d) 44
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 4 (b) 15 (c) 14 (d) 16
  21. 21.The numbers 14 to 22 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) 57 (c) 54 (d) 162
  22. 22.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 12 (c) 13 (d) 3
  24. 24.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) 60 (d) 57
  25. 25.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) 69 (b) 23 (c) 72 (d) 207
  26. 26.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) 117 (b) 13 (c) 39 (d) 42
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 17 (d) 6
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 3 (d) 1
  29. 29.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 438 (c) 550 (d) 549
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 4 (d) 2
  31. 31.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) 90 (b) 33 (c) 10 (d) 30
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  34. 34.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 94 (c) 93 (d) 102
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 15 (d) 4
  36. 36.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 457 (d) 456
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  38. 38.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 79 (c) 80 (d) 70
  39. 39.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 362 (c) 426 (d) 436
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 9 (c) 7 (d) 6

Answer key

  1. 145
  2. 51
  3. 264
  4. 16
  5. 228
  6. 189
  7. 390
  8. 6
  9. 2
  10. 17
  11. 5
  12. 6
  13. 507
  14. 19
  15. 19
  16. 33
  17. 9
  18. 4
  19. 43
  20. 15
  21. 54
  22. 312
  23. 13
  24. 57
  25. 69
  26. 39
  27. 16
  28. 3
  29. 549
  30. 4
  31. 30
  32. 2
  33. 9
  34. 93
  35. 15
  36. 456
  37. 8
  38. 79
  39. 435
  40. 9

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