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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 953 · 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 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
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 19 (d) 9
  3. 3.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) 55 (d) 56
  4. 4.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 133 (c) 134 (d) 124
  5. 5.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) 12 (b) 36 (c) 39 (d) 108
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 7 (b) 9 (c) 6 (d) 8
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 4 (d) 3
  8. 8.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) 216 (c) 24 (d) 72
  9. 9.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) 18 (c) 57 (d) 54
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 3 (b) 4 (c) 6 (d) 5
  12. 12.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 468 (c) 585 (d) 595
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 19 (d) 9
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  16. 16.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 160 (c) 170 (d) 178
  17. 17.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 198 (c) 208 (d) 210
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  19. 19.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) 66 (c) 63 (d) 189
  20. 20.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) 18 (c) 15 (d) 5
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  22. 22.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 543 (c) 544 (d) 534
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 20 (d) 9
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 18 (d) 19
  26. 26.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) 63 (d) 60
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 6 (b) 4 (c) 5 (d) 7
  28. 28.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 237 (c) 247 (d) 236
  29. 29.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) 171 (c) 57 (d) 19
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 6 (d) 5
  31. 31.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 549 (c) 558 (d) 444
  32. 32.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) 44 (d) 43
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 13 (c) 12 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 4 (b) 3 (c) 6 (d) 5
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 5 (b) 3 (c) 4 (d) 2
  38. 38.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 280 (c) 279 (d) 270
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17

Answer key

  1. 18
  2. 19
  3. 55
  4. 133
  5. 36
  6. 8
  7. 5
  8. 72
  9. 54
  10. 20
  11. 5
  12. 594
  13. 20
  14. 5
  15. 15
  16. 169
  17. 207
  18. 2
  19. 63
  20. 15
  21. 18
  22. 543
  23. 4
  24. 19
  25. 19
  26. 60
  27. 6
  28. 246
  29. 57
  30. 6
  31. 558
  32. 43
  33. 12
  34. 7
  35. 5
  36. 5
  37. 4
  38. 279
  39. 20
  40. 3

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