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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 115 · 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 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 166 (c) 165 (d) 156
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 4 (b) 6 (c) 5 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  5. 5.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) 81 (c) 27 (d) 30
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 6 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 3 (c) 15 (d) 13
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  13. 13.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 54 (c) 51 (d) 17
  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) 21 (c) 18 (d) 6
  15. 15.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) 135 (b) 15 (c) 45 (d) 48
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 19
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  18. 18.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 355 (c) 308 (d) 354
  19. 19.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 354 (c) 424 (d) 414
  20. 20.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 255 (c) 248 (d) 264
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 19 (d) 18
  22. 22.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 140 (c) 132 (d) 122
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 3 (c) 4 (d) 5
  25. 25.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 598 (c) 597 (d) 470
  26. 26.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 148 (c) 156 (d) 147
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 3 (c) 14 (d) 13
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 4 (d) 2
  29. 29.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 288 (c) 279 (d) 264
  30. 30.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 134 (d) 126
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 5 (c) 7 (d) 10
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 5 (c) 6 (d) 9
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 1
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 14 (d) 3
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 7 (d) 6
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 20 (d) 18
  37. 37.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 231 (c) 232 (d) 240
  38. 38.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) 57 (b) 19 (c) 60 (d) 171
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 1 (d) 4
  40. 40.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 32 (c) 50 (d) 42

Answer key

  1. 165
  2. 5
  3. 4
  4. 5
  5. 27
  6. 2
  7. 2
  8. 6
  9. 3
  10. 14
  11. 17
  12. 20
  13. 51
  14. 18
  15. 45
  16. 18
  17. 4
  18. 354
  19. 423
  20. 264
  21. 18
  22. 131
  23. 18
  24. 5
  25. 597
  26. 147
  27. 14
  28. 4
  29. 288
  30. 125
  31. 9
  32. 8
  33. 3
  34. 14
  35. 7
  36. 19
  37. 240
  38. 57
  39. 3
  40. 41

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