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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 347 · 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 4 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 21 (d) 20
  2. 2.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 540 (c) 550 (d) 438
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 15 (b) 16 (c) 14 (d) 4
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
  5. 5.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 142 (c) 132 (d) 150
  6. 6.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
  7. 7.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) 8 (b) 72 (c) 24 (d) 27
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 11 (b) 10 (c) 9 (d) 12
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 3 (d) 6
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 15 (b) 16 (c) 4 (d) 14
  11. 11.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) 108 (b) 12 (c) 39 (d) 36
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 5 (d) 2
  14. 14.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
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 3 (c) 14 (d) 15
  16. 16.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) 90 (b) 30 (c) 10 (d) 33
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 9 (c) 6 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 21 (d) 20
  20. 20.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 158 (c) 168 (d) 176
  21. 21.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 487 (c) 486 (d) 396
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 8 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  25. 25.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 597 (c) 607 (d) 606
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 4 (c) 3 (d) 5
  28. 28.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) 39 (b) 117 (c) 42 (d) 13
  29. 29.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 52 (c) 60 (d) 51
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  31. 31.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) 21 (b) 24 (c) 7 (d) 63
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  34. 34.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
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  36. 36.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 367 (c) 366 (d) 357
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  38. 38.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 391 (c) 332 (d) 381
  39. 39.The numbers 19 to 27 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) 72 (c) 23 (d) 207
  40. 40.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) 45 (b) 15 (c) 48 (d) 135

Answer key

  1. 20
  2. 549
  3. 15
  4. 18
  5. 141
  6. 66
  7. 24
  8. 11
  9. 5
  10. 15
  11. 36
  12. 4
  13. 4
  14. 60
  15. 14
  16. 30
  17. 8
  18. 4
  19. 20
  20. 167
  21. 486
  22. 19
  23. 7
  24. 7
  25. 606
  26. 2
  27. 4
  28. 39
  29. 51
  30. 6
  31. 21
  32. 9
  33. 4
  34. 57
  35. 3
  36. 366
  37. 5
  38. 390
  39. 69
  40. 45

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