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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 72 · 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 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 1 (c) 3 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 20 (b) 19 (c) 18 (d) 8
  4. 4.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
  5. 5.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 516 (c) 525 (d) 422
  6. 6.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) 33 (b) 11 (c) 99 (d) 36
  7. 7.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 486 (c) 622 (d) 621
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  9. 9.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 241 (c) 232 (d) 231
  10. 10.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 624 (c) 615 (d) 625
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 3 (d) 2
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 17 (d) 16
  14. 14.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 326 (d) 381
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
  16. 16.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) 24 (c) 7 (d) 63
  17. 17.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) 153 (b) 54 (c) 51 (d) 17
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  19. 19.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) 60 (b) 19 (c) 171 (d) 57
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  21. 21.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 108 (c) 116 (d) 98
  22. 22.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) 51 (b) 48 (c) 16 (d) 144
  23. 23.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
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 15 (c) 16 (d) 14
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 6 (d) 7
  27. 27.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) 9 (d) 81
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 20 (d) 19
  29. 29.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) 69 (c) 23 (d) 207
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 2 (d) 3
  31. 31.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 406 (c) 396 (d) 342
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 15 (c) 16 (d) 4
  34. 34.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 513 (c) 420 (d) 523
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 17 (c) 16 (d) 15
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 19 (d) 20
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 8 (d) 17
  38. 38.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  39. 39.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) 63 (b) 180 (c) 60 (d) 20
  40. 40.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 517 (c) 516 (d) 507

Answer key

  1. 3
  2. 5
  3. 19
  4. 66
  5. 525
  6. 33
  7. 621
  8. 2
  9. 240
  10. 624
  11. 4
  12. 2
  13. 17
  14. 381
  15. 3
  16. 21
  17. 51
  18. 3
  19. 57
  20. 4
  21. 107
  22. 48
  23. 30
  24. 8
  25. 15
  26. 6
  27. 27
  28. 19
  29. 69
  30. 4
  31. 405
  32. 9
  33. 15
  34. 522
  35. 16
  36. 19
  37. 18
  38. 6
  39. 60
  40. 516

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