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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 681 · 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 9 written when you write all the numbers from 1 to 97? (a) 9 (b) 17 (c) 15 (d) 18
  2. 2.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 357 (d) 358
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 9 (d) 19
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 14 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  7. 7.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 97 (c) 106 (d) 98
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 5 (b) 7 (c) 6 (d) 4
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 3 (d) 4
  12. 12.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
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 15 (d) 4
  14. 14.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) 54 (c) 162 (d) 18
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 18 (d) 16
  17. 17.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 304 (c) 339 (d) 349
  18. 18.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 127 (c) 118 (d) 136
  19. 19.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 378 (c) 324 (d) 369
  20. 20.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) 216 (b) 72 (c) 75 (d) 24
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 6 (b) 7 (c) 5 (d) 8
  22. 22.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 72 (d) 8
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  24. 24.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 622 (c) 486 (d) 612
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 21 (d) 19
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
  28. 28.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 555 (d) 546
  29. 29.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) 15 (b) 45 (c) 5 (d) 18
  30. 30.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) 10 (b) 33 (c) 90 (d) 30
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 5 (d) 3
  32. 32.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 144 (c) 153 (d) 162
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 19 (d) 20
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 4 (b) 7 (c) 5 (d) 6
  35. 35.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) 7 (b) 21 (c) 63 (d) 24
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 6 (d) 18
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 20 (d) 21
  38. 38.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  40. 40.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) 60 (c) 180 (d) 20

Answer key

  1. 17
  2. 357
  3. 6
  4. 19
  5. 15
  6. 8
  7. 97
  8. 2
  9. 7
  10. 6
  11. 5
  12. 19
  13. 15
  14. 54
  15. 6
  16. 17
  17. 348
  18. 127
  19. 378
  20. 72
  21. 7
  22. 24
  23. 3
  24. 621
  25. 7
  26. 20
  27. 3
  28. 555
  29. 15
  30. 30
  31. 5
  32. 153
  33. 20
  34. 6
  35. 21
  36. 17
  37. 20
  38. 9
  39. 4
  40. 60

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