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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 55 · 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 97? (a) 19 (b) 21 (c) 9 (d) 20
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  3. 3.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 480 (c) 481 (d) 471
  4. 4.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) 5 (c) 15 (d) 45
  5. 5.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 125 (d) 126
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 15 (b) 7 (c) 14 (d) 12
  8. 8.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 117 (c) 42 (d) 39
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 3 (d) 4
  11. 11.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) 144 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  13. 13.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 267 (c) 276 (d) 256
  14. 14.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 15 (c) 45 (d) 135
  15. 15.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 577 (c) 576 (d) 567
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  17. 17.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 414 (c) 405 (d) 348
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 3 (d) 5
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  21. 21.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 282 (c) 260 (d) 273
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 20 (d) 9
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 5 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  25. 25.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 156 (c) 148 (d) 138
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  28. 28.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 66 (c) 57 (d) 58
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 1 (d) 2
  30. 30.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) 54 (b) 51 (c) 153 (d) 17
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  32. 32.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 475 (c) 474 (d) 465
  33. 33.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) 27 (d) 81
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 10 (d) 3
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  37. 37.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) 45 (d) 42
  38. 38.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) 39 (b) 12 (c) 36 (d) 108
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 4 (d) 14

Answer key

  1. 20
  2. 15
  3. 480
  4. 15
  5. 125
  6. 6
  7. 14
  8. 39
  9. 3
  10. 5
  11. 48
  12. 2
  13. 276
  14. 45
  15. 576
  16. 20
  17. 414
  18. 5
  19. 9
  20. 4
  21. 282
  22. 19
  23. 5
  24. 4
  25. 147
  26. 7
  27. 6
  28. 57
  29. 3
  30. 51
  31. 5
  32. 474
  33. 27
  34. 9
  35. 10
  36. 20
  37. 42
  38. 36
  39. 17
  40. 15

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