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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 274 · 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 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 56 (c) 55 (d) 64
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  3. 3.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) 63 (c) 24 (d) 7
  4. 4.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) 218 (d) 219
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 5 (b) 4 (c) 3 (d) 6
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 4 (d) 5
  11. 11.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 262 (c) 252 (d) 261
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
  13. 13.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 621 (c) 612 (d) 486
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 15 (d) 14
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 3 (b) 6 (c) 5 (d) 4
  17. 17.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) 75 (b) 24 (c) 72 (d) 216
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 16 (c) 15 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  22. 22.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 534 (c) 535 (d) 525
  23. 23.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 424 (c) 423 (d) 414
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  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) 9 (c) 81 (d) 27
  26. 26.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) 14 (b) 126 (c) 42 (d) 45
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 9 (c) 16 (d) 19
  28. 28.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 344 (c) 399 (d) 408
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 3 (d) 2
  30. 30.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) 36 (b) 12 (c) 108 (d) 39
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 6 (c) 7 (d) 3
  32. 32.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) 17 (b) 153 (c) 51 (d) 54
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 3 (d) 1
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 14 (b) 13 (c) 12 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 9 (c) 15 (d) 13
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  39. 39.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) 63 (b) 189 (c) 66 (d) 21
  40. 40.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 92 (c) 91 (d) 82

Answer key

  1. 55
  2. 7
  3. 21
  4. 219
  5. 4
  6. 3
  7. 16
  8. 2
  9. 5
  10. 5
  11. 261
  12. 3
  13. 621
  14. 19
  15. 14
  16. 5
  17. 72
  18. 6
  19. 5
  20. 15
  21. 5
  22. 534
  23. 423
  24. 8
  25. 27
  26. 42
  27. 18
  28. 408
  29. 4
  30. 36
  31. 6
  32. 51
  33. 6
  34. 3
  35. 13
  36. 3
  37. 15
  38. 2
  39. 63
  40. 91

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