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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 720 · 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 4 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 18 (d) 16
  2. 2.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 472 (c) 471 (d) 386
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  4. 4.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) 90 (b) 10 (c) 30 (d) 33
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  7. 7.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) 81 (b) 30 (c) 9 (d) 27
  8. 8.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
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 5 (d) 16
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 4 (d) 1
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 5 (b) 7 (c) 6 (d) 8
  13. 13.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 213 (c) 222 (d) 223
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 20 (d) 19
  15. 15.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 202 (d) 201
  16. 16.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) 99 (b) 11 (c) 36 (d) 33
  17. 17.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 75 (d) 84
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 15 (d) 4
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
  20. 20.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 264 (c) 273 (d) 254
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 13
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 16 (d) 17
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 17 (b) 15 (c) 16 (d) 5
  26. 26.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 62 (c) 80 (d) 72
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 19 (d) 7
  28. 28.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) 256 (c) 276 (d) 267
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 3 (d) 4
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 8 (b) 10 (c) 7 (d) 9
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 15 (b) 13 (c) 6 (d) 14
  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) 21 (b) 18 (c) 54 (d) 6
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 16 (b) 17 (c) 15 (d) 5
  36. 36.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) 57 (c) 18 (d) 54
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
  38. 38.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) 8 (d) 72
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19
  40. 40.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) 45 (b) 15 (c) 18 (d) 5

Answer key

  1. 17
  2. 471
  3. 5
  4. 30
  5. 18
  6. 8
  7. 27
  8. 66
  9. 16
  10. 3
  11. 9
  12. 7
  13. 222
  14. 19
  15. 201
  16. 33
  17. 75
  18. 15
  19. 14
  20. 273
  21. 14
  22. 7
  23. 16
  24. 2
  25. 16
  26. 71
  27. 18
  28. 276
  29. 4
  30. 9
  31. 8
  32. 14
  33. 18
  34. 18
  35. 16
  36. 54
  37. 7
  38. 24
  39. 19
  40. 15

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