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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 621 · 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.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
  2. 2.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 320 (c) 363 (d) 372
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  5. 5.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 612 (c) 622 (d) 621
  6. 6.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 140 (c) 148 (d) 139
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 19 (b) 20 (c) 8 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  11. 11.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 40 (c) 30 (d) 48
  12. 12.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 520 (c) 418 (d) 519
  13. 13.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 196 (c) 187 (d) 178
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 16 (d) 15
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 6 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  22. 22.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 36 (d) 45
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 21 (d) 19
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 1
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 7 (d) 18
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 5 (d) 2
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  28. 28.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) 21 (b) 189 (c) 66 (d) 63
  29. 29.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 60 (c) 59 (d) 50
  30. 30.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 142 (c) 134 (d) 124
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 18
  32. 32.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) 48 (c) 15 (d) 45
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 10 (b) 9 (c) 11 (d) 8
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 20
  36. 36.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) 18 (b) 21 (c) 54 (d) 6
  37. 37.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 435 (c) 436 (d) 426
  38. 38.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 303 (c) 280 (d) 313
  39. 39.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) 17 (b) 51 (c) 54 (d) 153
  40. 40.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 102 (c) 94 (d) 84

Answer key

  1. 48
  2. 372
  3. 7
  4. 4
  5. 621
  6. 139
  7. 2
  8. 19
  9. 3
  10. 5
  11. 39
  12. 519
  13. 187
  14. 2
  15. 16
  16. 5
  17. 9
  18. 8
  19. 3
  20. 8
  21. 9
  22. 45
  23. 20
  24. 3
  25. 18
  26. 4
  27. 6
  28. 63
  29. 59
  30. 133
  31. 19
  32. 45
  33. 10
  34. 19
  35. 19
  36. 18
  37. 435
  38. 312
  39. 51
  40. 93

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