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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 635 · 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 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) 66 (c) 69 (d) 198
  2. 2.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) 20 (b) 180 (c) 60 (d) 63
  3. 3.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 19 (c) 171 (d) 57
  4. 4.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 68 (d) 58
  5. 5.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) 33 (d) 36
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  7. 7.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
  8. 8.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 492 (c) 483 (d) 493
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 15 (d) 16
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  13. 13.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 298 (c) 339 (d) 340
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  15. 15.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 168 (c) 176 (d) 167
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 17 (d) 15
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 15 (d) 14
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  20. 20.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 477 (d) 478
  21. 21.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  22. 22.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) 135 (b) 48 (c) 45 (d) 15
  23. 23.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 127 (c) 136 (d) 128
  24. 24.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) 42 (b) 45 (c) 14 (d) 126
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  26. 26.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 53 (c) 54 (d) 62
  27. 27.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) 90 (c) 30 (d) 33
  28. 28.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 81 (c) 72 (d) 90
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 4 (d) 5
  30. 30.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) 45 (d) 15
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  32. 32.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
  33. 33.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  34. 34.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 114 (c) 132 (d) 123
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 3 (d) 5
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  39. 39.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 366 (c) 322 (d) 375
  40. 40.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) 63 (b) 21 (c) 66 (d) 189

Answer key

  1. 66
  2. 60
  3. 57
  4. 67
  5. 33
  6. 3
  7. 72
  8. 492
  9. 5
  10. 15
  11. 16
  12. 8
  13. 339
  14. 2
  15. 167
  16. 3
  17. 16
  18. 15
  19. 2
  20. 477
  21. 8
  22. 45
  23. 127
  24. 42
  25. 5
  26. 53
  27. 30
  28. 81
  29. 5
  30. 15
  31. 6
  32. 24
  33. 6
  34. 123
  35. 9
  36. 5
  37. 4
  38. 3
  39. 375
  40. 63

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