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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 478 · 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 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 7 (d) 6
  2. 2.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) 297 (c) 307 (d) 306
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  4. 4.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 532 (b) 531 (c) 426 (d) 522
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
  6. 6.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) 15 (b) 45 (c) 135 (d) 48
  7. 7.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) 7 (b) 24 (c) 63 (d) 21
  8. 8.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 14 (c) 13 (d) 15
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  11. 11.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 183 (c) 174 (d) 184
  12. 12.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 630 (c) 631 (d) 621
  13. 13.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 240 (c) 241 (d) 232
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  15. 15.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 525 (c) 526 (d) 516
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  17. 17.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 184 (c) 175 (d) 166
  18. 18.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) 72 (b) 75 (c) 216 (d) 24
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  20. 20.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) 189 (b) 66 (c) 63 (d) 21
  21. 21.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 100 (c) 90 (d) 108
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  25. 25.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) 54 (c) 6 (d) 18
  26. 26.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 294 (c) 268 (d) 295
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  31. 31.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 328 (c) 290 (d) 318
  32. 32.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) 126 (b) 45 (c) 14 (d) 42
  33. 33.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 47 (c) 38 (d) 56
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 6 (d) 4
  35. 35.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) 33 (b) 10 (c) 30 (d) 90
  36. 36.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) 198 (b) 66 (c) 22 (d) 69
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 15 (c) 13 (d) 14
  38. 38.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) 171 (b) 60 (c) 19 (d) 57
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 15 (d) 14

Answer key

  1. 7
  2. 306
  3. 3
  4. 531
  5. 3
  6. 45
  7. 21
  8. 3
  9. 14
  10. 7
  11. 183
  12. 630
  13. 240
  14. 9
  15. 525
  16. 4
  17. 175
  18. 72
  19. 3
  20. 63
  21. 99
  22. 2
  23. 2
  24. 8
  25. 18
  26. 294
  27. 5
  28. 4
  29. 14
  30. 5
  31. 327
  32. 42
  33. 47
  34. 5
  35. 30
  36. 66
  37. 14
  38. 57
  39. 4
  40. 14

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