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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 169 · 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 5? (a) 5 (b) 6 (c) 4 (d) 10
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  4. 4.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) 23 (c) 207 (d) 72
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 1 (d) 3
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  7. 7.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 182 (d) 173
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 5 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  10. 10.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) 72 (b) 24 (c) 27 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  12. 12.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 40 (c) 32 (d) 22
  13. 13.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 408 (c) 409 (d) 344
  14. 14.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) 54 (b) 18 (c) 6 (d) 21
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  16. 16.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 537 (c) 436 (d) 547
  17. 17.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 309 (c) 319 (d) 284
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 5 (d) 4
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 15 (d) 4
  20. 20.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 420 (c) 358 (d) 430
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  22. 22.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 101 (c) 110 (d) 92
  23. 23.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 64 (d) 82
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  25. 25.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 98 (c) 108 (d) 116
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 12 (c) 3 (d) 11
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  29. 29.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 74 (c) 66 (d) 65
  30. 30.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) 48 (b) 16 (c) 144 (d) 51
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  32. 32.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) 63 (b) 180 (c) 60 (d) 20
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 4 (d) 5
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 18 (d) 17
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 16 (b) 15 (c) 4 (d) 14
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  37. 37.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) 15 (b) 5 (c) 45 (d) 18
  38. 38.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 496 (c) 636 (d) 637
  39. 39.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) 36 (b) 11 (c) 33 (d) 99
  40. 40.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) 18 (c) 57 (d) 54

Answer key

  1. 5
  2. 4
  3. 6
  4. 69
  5. 3
  6. 6
  7. 173
  8. 4
  9. 2
  10. 24
  11. 5
  12. 31
  13. 408
  14. 18
  15. 9
  16. 546
  17. 318
  18. 6
  19. 15
  20. 429
  21. 4
  22. 101
  23. 73
  24. 8
  25. 107
  26. 11
  27. 9
  28. 17
  29. 65
  30. 48
  31. 19
  32. 60
  33. 4
  34. 18
  35. 15
  36. 7
  37. 15
  38. 636
  39. 33
  40. 54

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