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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 104 · 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 two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  3. 3.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 367 (c) 316 (d) 357
  4. 4.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 477 (d) 478
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  6. 6.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) 63 (b) 66 (c) 21 (d) 189
  7. 7.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 54 (c) 62 (d) 44
  8. 8.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) 57 (d) 19
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  11. 11.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 272 (d) 291
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 20 (d) 21
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 4 (c) 16 (d) 15
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 17 (b) 16 (c) 18 (d) 6
  15. 15.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 258 (c) 244 (d) 249
  16. 16.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) 198 (d) 66
  17. 17.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 48 (d) 144
  18. 18.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) 30 (c) 27 (d) 81
  19. 19.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
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 5 (b) 2 (c) 4 (d) 3
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 9 (c) 7 (d) 8
  22. 22.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 423 (c) 360 (d) 433
  23. 23.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  24. 24.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) 33 (d) 36
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 3 (d) 6
  26. 26.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 586 (c) 576 (d) 462
  27. 27.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 604 (c) 603 (d) 594
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 18 (d) 7
  29. 29.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) 108 (c) 90 (d) 100
  30. 30.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) 23 (b) 69 (c) 207 (d) 72
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 15 (d) 14
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 10 (c) 11 (d) 7
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  34. 34.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 210 (d) 211
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 4 (b) 6 (c) 7 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 3 (d) 2
  38. 38.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) 135 (c) 48 (d) 15
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 18 (d) 20
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 21 (d) 9

Answer key

  1. 8
  2. 5
  3. 366
  4. 477
  5. 3
  6. 63
  7. 53
  8. 57
  9. 4
  10. 9
  11. 300
  12. 20
  13. 15
  14. 17
  15. 258
  16. 66
  17. 48
  18. 27
  19. 72
  20. 4
  21. 8
  22. 432
  23. 9
  24. 33
  25. 5
  26. 585
  27. 603
  28. 18
  29. 99
  30. 69
  31. 14
  32. 10
  33. 18
  34. 210
  35. 6
  36. 5
  37. 4
  38. 45
  39. 19
  40. 20

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