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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 161 · 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 12? (a) 13 (b) 8 (c) 6 (d) 7
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 15 (d) 16
  3. 3.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 504 (c) 513 (d) 414
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 58? (a) 17 (b) 16 (c) 15 (d) 5
  5. 5.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 113 (c) 114 (d) 104
  6. 6.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 346 (c) 402 (d) 412
  7. 7.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 108 (c) 98 (d) 107
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 10 (b) 11 (c) 9 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  12. 12.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) 20 (c) 180 (d) 60
  13. 13.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) 24 (b) 72 (c) 216 (d) 75
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 4 (c) 14 (d) 15
  15. 15.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) 69 (c) 198 (d) 66
  16. 16.The numbers 10 to 18 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) 42 (c) 126 (d) 14
  17. 17.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) 138 (c) 147 (d) 156
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 2 (d) 4
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 18 (d) 7
  21. 21.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 642 (c) 643 (d) 633
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 5 (b) 4 (c) 6 (d) 3
  23. 23.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) 144 (d) 48
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  25. 25.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 621 (c) 630 (d) 492
  26. 26.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
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  28. 28.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 448 (c) 564 (d) 565
  29. 29.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 380 (c) 462 (d) 453
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 15 (b) 14 (c) 16 (d) 5
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 4 (b) 2 (c) 3 (d) 5
  32. 32.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 33 (d) 30
  33. 33.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 31 (d) 40
  34. 34.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 589 (c) 464 (d) 579
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 18 (d) 16
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 16 (c) 5 (d) 15
  37. 37.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 188 (c) 178 (d) 196
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
  39. 39.The numbers 8 to 16 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) 12 (c) 108 (d) 39
  40. 40.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) 36 (c) 11 (d) 33

Answer key

  1. 7
  2. 16
  3. 513
  4. 16
  5. 113
  6. 411
  7. 107
  8. 4
  9. 3
  10. 10
  11. 6
  12. 60
  13. 72
  14. 14
  15. 66
  16. 42
  17. 147
  18. 3
  19. 9
  20. 18
  21. 642
  22. 5
  23. 48
  24. 4
  25. 630
  26. 24
  27. 9
  28. 564
  29. 462
  30. 15
  31. 4
  32. 30
  33. 31
  34. 588
  35. 17
  36. 15
  37. 187
  38. 4
  39. 36
  40. 33

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