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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 551 · 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 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 249 (c) 240 (d) 250
  2. 2.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 360 (c) 433 (d) 423
  3. 3.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 42 (c) 117 (d) 13
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  5. 5.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 426 (c) 427 (d) 417
  6. 6.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  8. 8.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 543 (c) 440 (d) 552
  9. 9.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) 23 (b) 72 (c) 69 (d) 207
  10. 10.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) 63 (c) 189 (d) 66
  11. 11.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) 54 (d) 162
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 21
  13. 13.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) 5 (b) 15 (c) 45 (d) 18
  14. 14.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 523 (d) 420
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 16 (c) 17 (d) 6
  16. 16.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) 10 (b) 30 (c) 33 (d) 90
  17. 17.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 114 (d) 113
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  19. 19.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) 33 (b) 11 (c) 99 (d) 36
  20. 20.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) 14 (c) 126 (d) 42
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 9 (b) 6 (c) 7 (d) 8
  23. 23.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 56 (c) 74 (d) 65
  24. 24.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) 216 (b) 24 (c) 75 (d) 72
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 5 (d) 3
  26. 26.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 411 (c) 412 (d) 402
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 18 (c) 17 (d) 6
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
  30. 30.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 24 (c) 42 (d) 34
  31. 31.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 158 (c) 167 (d) 176
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  34. 34.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 538 (c) 528 (d) 537
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 16 (c) 14 (d) 4
  37. 37.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) 69 (b) 198 (c) 66 (d) 22
  38. 38.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 67 (c) 68 (d) 76
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 18 (d) 6

Answer key

  1. 249
  2. 432
  3. 39
  4. 4
  5. 426
  6. 117
  7. 7
  8. 552
  9. 69
  10. 63
  11. 54
  12. 20
  13. 15
  14. 522
  15. 16
  16. 30
  17. 113
  18. 18
  19. 33
  20. 42
  21. 2
  22. 8
  23. 65
  24. 72
  25. 4
  26. 411
  27. 3
  28. 17
  29. 15
  30. 33
  31. 167
  32. 7
  33. 8
  34. 537
  35. 5
  36. 15
  37. 66
  38. 67
  39. 5
  40. 17

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