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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 427 · 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 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) 63 (b) 66 (c) 21 (d) 189
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  3. 3.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
  4. 4.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 100 (c) 110 (d) 109
  5. 5.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 538 (d) 537
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 16 (b) 7 (c) 17 (d) 18
  7. 7.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) 84 (c) 102 (d) 94
  8. 8.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 402 (c) 496 (d) 495
  9. 9.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
  10. 10.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) 69 (c) 207 (d) 72
  11. 11.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 164 (c) 155 (d) 156
  12. 12.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 300 (d) 301
  13. 13.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) 66 (c) 69 (d) 198
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 7 (b) 6 (c) 8 (d) 5
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 4 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  17. 17.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) 42 (b) 117 (c) 39 (d) 13
  18. 18.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 247 (c) 246 (d) 237
  19. 19.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 476 (d) 606
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 5
  21. 21.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) 90 (c) 30 (d) 33
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 13 (c) 15 (d) 14
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  25. 25.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 526 (c) 422 (d) 525
  26. 26.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) 45 (b) 15 (c) 18 (d) 5
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 6 (b) 4 (c) 5 (d) 7
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  30. 30.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) 144 (b) 16 (c) 51 (d) 48
  31. 31.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 99 (c) 90 (d) 100
  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) 15 (c) 48 (d) 45
  33. 33.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) 63 (b) 7 (c) 24 (d) 21
  34. 34.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 421 (c) 352 (d) 411
  35. 35.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 66 (c) 56 (d) 74
  36. 36.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) 42 (b) 45 (c) 126 (d) 14
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  38. 38.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 179 (c) 170 (d) 180
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
  40. 40.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 531 (c) 540 (d) 432

Answer key

  1. 63
  2. 6
  3. 18
  4. 109
  5. 537
  6. 17
  7. 93
  8. 495
  9. 72
  10. 69
  11. 155
  12. 300
  13. 66
  14. 7
  15. 5
  16. 2
  17. 39
  18. 246
  19. 606
  20. 4
  21. 30
  22. 17
  23. 14
  24. 5
  25. 525
  26. 15
  27. 6
  28. 15
  29. 18
  30. 48
  31. 99
  32. 45
  33. 21
  34. 420
  35. 65
  36. 42
  37. 3
  38. 179
  39. 3
  40. 540

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