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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 339 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 15 (d) 17
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 18
  5. 5.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) 21 (b) 189 (c) 66 (d) 63
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 17 (d) 16
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  8. 8.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 271 (c) 252 (d) 270
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 6 (d) 16
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 9 (b) 8 (c) 6 (d) 7
  11. 11.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) 166 (d) 176
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 4 (d) 16
  13. 13.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 7 (c) 24 (d) 63
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 16 (d) 17
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 5 (d) 2
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 17 (d) 18
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 14 (c) 13 (d) 15
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  21. 21.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 625 (c) 488 (d) 624
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  23. 23.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 210 (c) 219 (d) 218
  24. 24.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) 72 (b) 23 (c) 207 (d) 69
  25. 25.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) 27 (c) 81 (d) 9
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 11 (b) 6 (c) 10 (d) 8
  27. 27.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 439 (d) 438
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 15 (d) 16
  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) 57 (b) 18 (c) 54 (d) 162
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  31. 31.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 373 (c) 372 (d) 320
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 4 (d) 2
  33. 33.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) 15 (c) 5 (d) 45
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 20 (d) 18
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  37. 37.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) 33 (b) 90 (c) 10 (d) 30
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 5 (b) 7 (c) 6 (d) 4
  39. 39.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 460 (c) 582 (d) 573
  40. 40.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 264 (c) 273 (d) 274

Answer key

  1. 16
  2. 18
  3. 5
  4. 19
  5. 63
  6. 16
  7. 2
  8. 270
  9. 17
  10. 8
  11. 175
  12. 15
  13. 21
  14. 3
  15. 17
  16. 4
  17. 8
  18. 17
  19. 14
  20. 7
  21. 624
  22. 6
  23. 219
  24. 69
  25. 27
  26. 10
  27. 438
  28. 16
  29. 54
  30. 4
  31. 372
  32. 3
  33. 15
  34. 15
  35. 19
  36. 4
  37. 30
  38. 6
  39. 582
  40. 273

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