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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 8 · 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 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 523 (c) 522 (d) 420
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 15 (d) 6
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 5 (c) 4 (d) 3
  4. 4.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 94 (c) 104 (d) 103
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
  10. 10.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) 135 (c) 48 (d) 45
  11. 11.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) 232 (c) 241 (d) 240
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 4 (d) 1
  13. 13.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
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  15. 15.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 451 (c) 450 (d) 441
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 17 (d) 8
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 6 (c) 4 (d) 3
  19. 19.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) 75 (c) 24 (d) 216
  20. 20.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 520 (c) 519 (d) 418
  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) 54 (b) 17 (c) 51 (d) 153
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  23. 23.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 546 (c) 547 (d) 537
  24. 24.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) 144 (b) 16 (c) 51 (d) 48
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 4 (d) 15
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  29. 29.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 152 (c) 162 (d) 161
  30. 30.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 382 (c) 456 (d) 466
  31. 31.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 420 (c) 352 (d) 411
  32. 32.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 366 (c) 375 (d) 376
  33. 33.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) 441 (c) 442 (d) 366
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 5 (c) 7 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 13 (d) 15
  37. 37.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) 81 (c) 27 (d) 9
  38. 38.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) 42 (b) 126 (c) 45 (d) 14
  39. 39.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 231 (c) 232 (d) 222
  40. 40.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) 22 (d) 66

Answer key

  1. 522
  2. 16
  3. 4
  4. 103
  5. 6
  6. 57
  7. 7
  8. 8
  9. 5
  10. 45
  11. 240
  12. 3
  13. 33
  14. 2
  15. 450
  16. 18
  17. 2
  18. 5
  19. 72
  20. 519
  21. 51
  22. 7
  23. 546
  24. 48
  25. 9
  26. 15
  27. 3
  28. 8
  29. 161
  30. 465
  31. 420
  32. 375
  33. 441
  34. 7
  35. 4
  36. 14
  37. 27
  38. 42
  39. 231
  40. 66

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