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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 419 · 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.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) 108 (b) 12 (c) 39 (d) 36
  2. 2.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) 9 (b) 30 (c) 81 (d) 27
  3. 3.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) 24 (c) 75 (d) 72
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 4 (d) 6
  5. 5.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) 42 (b) 117 (c) 13 (d) 39
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 8 (b) 20 (c) 19 (d) 18
  9. 9.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
  10. 10.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 88 (c) 96 (d) 78
  11. 11.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 142 (c) 150 (d) 132
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
  13. 13.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 52 (c) 43 (d) 44
  14. 14.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 12 (b) 7 (c) 14 (d) 15
  16. 16.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 378 (c) 369 (d) 379
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 15 (b) 13 (c) 14 (d) 5
  18. 18.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 46 (c) 56 (d) 55
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 12 (d) 11
  22. 22.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) 180 (b) 20 (c) 60 (d) 63
  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) 162 (b) 54 (c) 18 (d) 57
  24. 24.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 375 (c) 384 (d) 328
  25. 25.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) 45 (b) 135 (c) 48 (d) 15
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 17 (d) 15
  27. 27.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) 72 (b) 27 (c) 8 (d) 24
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 18 (d) 9
  29. 29.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 78 (c) 77 (d) 68
  30. 30.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 161 (c) 170 (d) 152
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 4 (d) 2
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  33. 33.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 79 (d) 88
  34. 34.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) 22 (b) 198 (c) 69 (d) 66
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 5 (d) 6
  36. 36.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) 18 (c) 45 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  39. 39.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 283 (c) 260 (d) 273
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18

Answer key

  1. 36
  2. 27
  3. 72
  4. 5
  5. 39
  6. 6
  7. 5
  8. 19
  9. 30
  10. 87
  11. 141
  12. 20
  13. 43
  14. 7
  15. 14
  16. 378
  17. 14
  18. 55
  19. 2
  20. 9
  21. 12
  22. 60
  23. 54
  24. 384
  25. 45
  26. 16
  27. 24
  28. 19
  29. 77
  30. 161
  31. 4
  32. 4
  33. 79
  34. 66
  35. 5
  36. 15
  37. 3
  38. 3
  39. 282
  40. 2

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