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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 758 · 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) 51 (c) 17 (d) 153
  2. 2.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) 13 (b) 39 (c) 117 (d) 42
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 18 (d) 20
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  6. 6.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 517 (d) 516
  7. 7.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) 54 (b) 57 (c) 162 (d) 18
  8. 8.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 609 (d) 478
  9. 9.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 38 (d) 47
  10. 10.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 119 (c) 110 (d) 128
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 17 (d) 16
  12. 12.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 216 (c) 75 (d) 24
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 18 (d) 7
  14. 14.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) 36 (c) 99 (d) 33
  15. 15.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) 66 (c) 69 (d) 22
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 19 (d) 20
  18. 18.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) 48 (c) 135 (d) 45
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  20. 20.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 309 (c) 319 (d) 318
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  22. 22.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) 30 (b) 9 (c) 27 (d) 81
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 13 (d) 14
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  25. 25.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) 20 (b) 63 (c) 180 (d) 60
  26. 26.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 58 (c) 49 (d) 40
  27. 27.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 172 (c) 190 (d) 181
  28. 28.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) 57 (b) 171 (c) 60 (d) 19
  29. 29.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 486 (c) 495 (d) 402
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 2 (d) 1
  31. 31.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) 34 (c) 52 (d) 44
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  33. 33.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 302 (c) 346 (d) 345
  34. 34.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 1 (d) 4
  36. 36.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 315 (c) 325 (d) 324
  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) 159 (b) 168 (c) 160 (d) 150
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 5 (b) 6 (c) 4 (d) 3
  39. 39.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) 72 (c) 24 (d) 27
  40. 40.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 363 (c) 354 (d) 314

Answer key

  1. 51
  2. 39
  3. 5
  4. 19
  5. 4
  6. 516
  7. 54
  8. 609
  9. 47
  10. 119
  11. 17
  12. 72
  13. 18
  14. 33
  15. 66
  16. 8
  17. 19
  18. 45
  19. 7
  20. 318
  21. 6
  22. 27
  23. 14
  24. 3
  25. 60
  26. 49
  27. 181
  28. 57
  29. 495
  30. 3
  31. 43
  32. 5
  33. 345
  34. 141
  35. 3
  36. 324
  37. 159
  38. 5
  39. 24
  40. 363

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