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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 881 · 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 40? (a) 4 (b) 5 (c) 6 (d) 3
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 5 (d) 2
  3. 3.The numbers 19 to 27 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) 23 (c) 207 (d) 72
  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.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 9 (c) 19 (d) 20
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  9. 9.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 306 (c) 307 (d) 297
  10. 10.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 244 (c) 258 (d) 249
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 2 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 6 (b) 5 (c) 7 (d) 4
  14. 14.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) 21 (b) 189 (c) 63 (d) 66
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 7 (c) 6 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 9 (b) 10 (c) 11 (d) 8
  18. 18.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) 7 (d) 24
  19. 19.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 54 (c) 72 (d) 64
  20. 20.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) 42 (c) 126 (d) 45
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  22. 22.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 115 (c) 124 (d) 106
  23. 23.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) 18 (b) 54 (c) 57 (d) 162
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  26. 26.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 456 (c) 576 (d) 567
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  28. 28.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) 6 (b) 21 (c) 54 (d) 18
  29. 29.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 312 (c) 361 (d) 360
  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) 90 (b) 30 (c) 33 (d) 10
  31. 31.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 247 (c) 246 (d) 236
  32. 32.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 52 (d) 61
  33. 33.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) 39 (c) 117 (d) 42
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 7 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  37. 37.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
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 18 (b) 17 (c) 8 (d) 19
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 2 (d) 4
  40. 40.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) 66 (b) 69 (c) 22 (d) 198

Answer key

  1. 5
  2. 4
  3. 69
  4. 15
  5. 18
  6. 8
  7. 20
  8. 6
  9. 306
  10. 258
  11. 4
  12. 5
  13. 6
  14. 63
  15. 8
  16. 7
  17. 10
  18. 21
  19. 63
  20. 42
  21. 9
  22. 115
  23. 54
  24. 2
  25. 20
  26. 576
  27. 2
  28. 18
  29. 360
  30. 30
  31. 246
  32. 61
  33. 39
  34. 7
  35. 7
  36. 6
  37. 72
  38. 18
  39. 4
  40. 66

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