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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 811 · 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) 21 (b) 6 (c) 18 (d) 54
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 14 (b) 5 (c) 16 (d) 15
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 2 (d) 3
  4. 4.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 306 (c) 342 (d) 352
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  6. 6.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
  7. 7.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 500 (c) 642 (d) 633
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 5 (d) 8
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 14 (d) 13
  12. 12.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) 57 (c) 54 (d) 18
  13. 13.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 30 (c) 39 (d) 48
  14. 14.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) 189 (c) 63 (d) 66
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  16. 16.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) 36 (d) 33
  17. 17.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) 60 (b) 63 (c) 180 (d) 20
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 19 (d) 8
  19. 19.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 454 (c) 444 (d) 453
  20. 20.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) 24 (b) 21 (c) 63 (d) 7
  21. 21.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) 8 (d) 72
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
  24. 24.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) 13 (b) 39 (c) 42 (d) 117
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 7 (c) 9 (d) 8
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 5 (b) 7 (c) 6 (d) 8
  28. 28.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 172 (d) 163
  29. 29.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 579 (d) 458
  30. 30.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
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 17 (d) 15
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 7 (b) 5 (c) 6 (d) 8
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 9 (b) 6 (c) 5 (d) 8
  34. 34.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 15 (c) 17 (d) 16
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 16 (c) 6 (d) 17
  37. 37.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 489 (c) 499 (d) 498
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 20 (b) 19 (c) 9 (d) 18
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 20 (d) 19

Answer key

  1. 18
  2. 15
  3. 4
  4. 351
  5. 5
  6. 15
  7. 642
  8. 7
  9. 5
  10. 9
  11. 14
  12. 54
  13. 39
  14. 63
  15. 4
  16. 33
  17. 60
  18. 19
  19. 453
  20. 21
  21. 24
  22. 19
  23. 15
  24. 39
  25. 8
  26. 3
  27. 7
  28. 163
  29. 579
  30. 66
  31. 16
  32. 7
  33. 8
  34. 378
  35. 16
  36. 16
  37. 498
  38. 19
  39. 3
  40. 19

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