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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 195 · 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 6 written when you write all the numbers from 1 to 75? (a) 7 (b) 16 (c) 18 (d) 17
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  3. 3.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) 17 (c) 51 (d) 54
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 17 (d) 7
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  6. 6.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 282 (c) 283 (d) 260
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 18 (d) 16
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  9. 9.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) 162 (b) 18 (c) 54 (d) 57
  10. 10.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 555 (c) 556 (d) 442
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  12. 12.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) 615 (c) 625 (d) 624
  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) 99 (c) 33 (d) 36
  14. 14.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 76 (d) 75
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 5 (c) 6 (d) 7
  17. 17.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 109 (c) 110 (d) 100
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  20. 20.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 294 (d) 274
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 8 (c) 6 (d) 7
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 16 (d) 6
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 9 (b) 11 (c) 14 (d) 13
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  25. 25.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) 51 (c) 48 (d) 16
  26. 26.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 448 (c) 564 (d) 555
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 3 (d) 5
  29. 29.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 12 (d) 39
  30. 30.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 26 (c) 44 (d) 36
  31. 31.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 65 (c) 56 (d) 74
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 16 (c) 17 (d) 15
  33. 33.The numbers 2 to 10 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) 21 (c) 6 (d) 18
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  35. 35.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 77 (c) 78 (d) 86
  36. 36.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) 45 (b) 14 (c) 42 (d) 126
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 5 (b) 3 (c) 6 (d) 4
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 5 (b) 4 (c) 6 (d) 3
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  40. 40.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

Answer key

  1. 17
  2. 3
  3. 51
  4. 17
  5. 7
  6. 282
  7. 17
  8. 17
  9. 54
  10. 555
  11. 18
  12. 624
  13. 33
  14. 75
  15. 9
  16. 6
  17. 109
  18. 6
  19. 19
  20. 303
  21. 8
  22. 17
  23. 13
  24. 4
  25. 48
  26. 564
  27. 20
  28. 5
  29. 36
  30. 35
  31. 65
  32. 16
  33. 18
  34. 19
  35. 77
  36. 42
  37. 5
  38. 5
  39. 7
  40. 519

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