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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 914 · 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 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 36 (c) 26 (d) 44
  2. 2.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 28 (d) 46
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 19 (d) 8
  6. 6.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) 63 (c) 7 (d) 21
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 17
  8. 8.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 430 (d) 429
  9. 9.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 136 (d) 126
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 3 (b) 5 (c) 4 (d) 2
  11. 11.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) 8 (c) 24 (d) 72
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 2 (d) 3
  15. 15.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 411 (c) 421 (d) 420
  16. 16.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
  17. 17.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) 66 (d) 69
  18. 18.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 138 (c) 137 (d) 146
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  20. 20.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 82 (c) 74 (d) 64
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  22. 22.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) 18 (b) 45 (c) 5 (d) 15
  23. 23.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) 66 (b) 63 (c) 21 (d) 189
  24. 24.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 204 (c) 198 (d) 199
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 10 (b) 9 (c) 8 (d) 7
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 16 (d) 6
  28. 28.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 156 (c) 147 (d) 138
  29. 29.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) 15 (b) 48 (c) 135 (d) 45
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 6 (d) 5
  32. 32.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 490 (c) 628 (d) 618
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 18 (d) 8
  34. 34.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) 11 (b) 33 (c) 99 (d) 36
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 4 (d) 5
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
  37. 37.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 381 (c) 372 (d) 382
  38. 38.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 17 (b) 5 (c) 15 (d) 16
  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) 57 (b) 18 (c) 162 (d) 54

Answer key

  1. 35
  2. 37
  3. 17
  4. 5
  5. 19
  6. 21
  7. 18
  8. 429
  9. 135
  10. 4
  11. 24
  12. 6
  13. 4
  14. 4
  15. 420
  16. 151
  17. 66
  18. 137
  19. 4
  20. 73
  21. 9
  22. 15
  23. 63
  24. 198
  25. 8
  26. 9
  27. 17
  28. 147
  29. 45
  30. 3
  31. 5
  32. 627
  33. 18
  34. 33
  35. 4
  36. 4
  37. 381
  38. 5
  39. 16
  40. 54

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