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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 628 · 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 times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 13 (d) 15
  2. 2.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) 33 (c) 11 (d) 36
  3. 3.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) 24 (b) 72 (c) 8 (d) 27
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  5. 5.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) 189 (b) 21 (c) 66 (d) 63
  6. 6.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 368 (d) 444
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
  8. 8.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) 30 (b) 27 (c) 9 (d) 81
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
  10. 10.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 508 (c) 507 (d) 410
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  13. 13.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 33 (d) 42
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 13 (c) 7 (d) 10
  15. 15.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) 519 (d) 418
  16. 16.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) 525 (d) 422
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  18. 18.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 122 (c) 104 (d) 113
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  21. 21.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 597 (c) 606 (d) 607
  22. 22.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) 6 (b) 18 (c) 21 (d) 54
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  24. 24.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) 12 (b) 39 (c) 108 (d) 36
  25. 25.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 388 (c) 475 (d) 474
  26. 26.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 44 (c) 34 (d) 43
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  28. 28.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 415 (c) 348 (d) 405
  29. 29.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 450 (c) 558 (d) 567
  30. 30.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) 20 (b) 60 (c) 63 (d) 180
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 15 (d) 16
  32. 32.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) 18 (b) 15 (c) 45 (d) 5
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 17 (b) 15 (c) 16 (d) 6
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 6 (b) 7 (c) 5 (d) 4
  35. 35.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) 162 (b) 54 (c) 57 (d) 18
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 2 (d) 3
  37. 37.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) 14 (c) 45 (d) 126
  38. 38.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 196 (c) 186 (d) 195
  39. 39.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) 24 (b) 7 (c) 21 (d) 63
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 20 (d) 9

Answer key

  1. 14
  2. 33
  3. 24
  4. 6
  5. 63
  6. 444
  7. 3
  8. 27
  9. 19
  10. 507
  11. 6
  12. 8
  13. 33
  14. 12
  15. 519
  16. 525
  17. 4
  18. 113
  19. 3
  20. 4
  21. 606
  22. 18
  23. 5
  24. 36
  25. 474
  26. 43
  27. 17
  28. 414
  29. 567
  30. 60
  31. 15
  32. 15
  33. 16
  34. 6
  35. 54
  36. 4
  37. 42
  38. 195
  39. 21
  40. 19

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