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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 619 · 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 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) 63 (b) 21 (c) 66 (d) 189
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  5. 5.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 406 (c) 501 (d) 502
  6. 6.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) 9 (c) 30 (d) 81
  7. 7.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 424 (c) 519 (d) 528
  8. 8.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 106 (c) 114 (d) 105
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 17 (d) 19
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  13. 13.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 327 (c) 296 (d) 337
  14. 14.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 92 (d) 101
  15. 15.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) 18 (b) 5 (c) 15 (d) 45
  16. 16.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 549 (c) 444 (d) 558
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  18. 18.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 476 (c) 607 (d) 597
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 4 (d) 16
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  21. 21.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 241 (c) 240 (d) 232
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 4 (d) 1
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  29. 29.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) 162 (b) 18 (c) 57 (d) 54
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  32. 32.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 184 (c) 176 (d) 166
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
  34. 34.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) 33 (c) 36 (d) 99
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 17 (d) 16
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 15 (d) 4
  37. 37.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 168 (d) 150
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 16 (c) 18 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  40. 40.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 264 (c) 248 (d) 265

Answer key

  1. 63
  2. 2
  3. 3
  4. 5
  5. 501
  6. 27
  7. 528
  8. 105
  9. 18
  10. 9
  11. 7
  12. 19
  13. 336
  14. 101
  15. 15
  16. 558
  17. 6
  18. 606
  19. 15
  20. 9
  21. 240
  22. 3
  23. 8
  24. 3
  25. 4
  26. 8
  27. 5
  28. 3
  29. 54
  30. 19
  31. 5
  32. 175
  33. 3
  34. 33
  35. 16
  36. 15
  37. 159
  38. 17
  39. 4
  40. 264

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