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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 457 · 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 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 218 (c) 210 (d) 220
  2. 2.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) 66 (b) 63 (c) 21 (d) 189
  3. 3.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) 352 (c) 411 (d) 420
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 6 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 15 (d) 17
  8. 8.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 74 (c) 83 (d) 92
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 5 (d) 3
  11. 11.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 217 (c) 216 (d) 207
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  13. 13.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
  14. 14.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) 69 (b) 66 (c) 198 (d) 22
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  16. 16.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 306 (c) 315 (d) 316
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 15 (c) 14 (d) 3
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 19 (d) 18
  20. 20.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 529 (c) 424 (d) 519
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 21 (d) 20
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  24. 24.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 406 (c) 405 (d) 396
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 6 (b) 7 (c) 5 (d) 4
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 19 (d) 18
  28. 28.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 537 (d) 538
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 20 (d) 19
  30. 30.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 313 (c) 303 (d) 312
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 7 (d) 19
  34. 34.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) 60 (d) 180
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 5 (d) 7
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 6 (d) 16
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 4 (d) 5
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 3 (d) 5
  40. 40.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) 90 (c) 30 (d) 33

Answer key

  1. 219
  2. 63
  3. 420
  4. 5
  5. 2
  6. 8
  7. 16
  8. 83
  9. 4
  10. 5
  11. 216
  12. 15
  13. 27
  14. 66
  15. 7
  16. 315
  17. 6
  18. 14
  19. 18
  20. 528
  21. 2
  22. 20
  23. 5
  24. 405
  25. 9
  26. 6
  27. 18
  28. 537
  29. 20
  30. 312
  31. 9
  32. 3
  33. 18
  34. 60
  35. 6
  36. 6
  37. 17
  38. 5
  39. 4
  40. 30

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