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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 100 · 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.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 51 (c) 52 (d) 42
  2. 2.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
  3. 3.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 152 (c) 151 (d) 142
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 18 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  6. 6.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 300 (d) 343
  7. 7.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) 81 (c) 30 (d) 27
  8. 8.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 294 (c) 274 (d) 304
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 6 (b) 4 (c) 5 (d) 3
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 19 (d) 18
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 7 (d) 8
  12. 12.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 387 (c) 330 (d) 378
  13. 13.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 153 (c) 154 (d) 162
  14. 14.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 54 (d) 72
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  16. 16.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) 63 (c) 180 (d) 60
  17. 17.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 444 (c) 559 (d) 558
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 17 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  20. 20.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) 30 (b) 33 (c) 10 (d) 90
  21. 21.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 432 (c) 433 (d) 360
  22. 22.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 430 (c) 429 (d) 358
  23. 23.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 60 (c) 68 (d) 59
  24. 24.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) 18 (b) 21 (c) 6 (d) 54
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 19 (b) 18 (c) 20 (d) 9
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 16 (d) 15
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 19
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 4 (d) 3
  33. 33.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) 69 (b) 22 (c) 66 (d) 198
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 16 (b) 18 (c) 7 (d) 17
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 20 (d) 9
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 21
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 8 (b) 5 (c) 6 (d) 7
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9

Answer key

  1. 51
  2. 72
  3. 151
  4. 19
  5. 3
  6. 342
  7. 27
  8. 303
  9. 5
  10. 19
  11. 8
  12. 387
  13. 153
  14. 63
  15. 9
  16. 60
  17. 558
  18. 18
  19. 2
  20. 30
  21. 432
  22. 429
  23. 59
  24. 18
  25. 19
  26. 7
  27. 6
  28. 5
  29. 15
  30. 18
  31. 8
  32. 4
  33. 66
  34. 17
  35. 5
  36. 20
  37. 20
  38. 2
  39. 7
  40. 19

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