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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 578 · 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) 144 (b) 48 (c) 51 (d) 16
  2. 2.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 471 (c) 481 (d) 392
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  4. 4.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
  5. 5.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 44 (c) 36 (d) 35
  6. 6.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 400 (c) 483 (d) 493
  7. 7.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) 54 (b) 51 (c) 17 (d) 153
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 8 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 6 (d) 5
  12. 12.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) 66 (c) 63 (d) 21
  13. 13.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  14. 14.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 71 (c) 62 (d) 80
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 9 (b) 11 (c) 10 (d) 8
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 8 (b) 7 (c) 10 (d) 9
  17. 17.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) 216 (c) 72 (d) 75
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 3 (c) 15 (d) 14
  19. 19.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) 462 (c) 380 (d) 453
  20. 20.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 451 (c) 372 (d) 450
  21. 21.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 139 (c) 148 (d) 130
  22. 22.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 339 (c) 340 (d) 330
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 1 (d) 2
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 3 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 8 (d) 19
  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) 24 (b) 8 (c) 72 (d) 27
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 19 (d) 7
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 5 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  31. 31.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 115 (c) 124 (d) 106
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 13 (c) 3 (d) 14
  34. 34.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 577 (c) 456 (d) 576
  35. 35.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) 114 (c) 113 (d) 104
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  37. 37.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 516 (c) 507 (d) 416
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  39. 39.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 376 (c) 457 (d) 456
  40. 40.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) 33 (b) 10 (c) 90 (d) 30

Answer key

  1. 48
  2. 480
  3. 2
  4. 18
  5. 35
  6. 492
  7. 51
  8. 6
  9. 18
  10. 8
  11. 5
  12. 63
  13. 9
  14. 71
  15. 10
  16. 9
  17. 72
  18. 14
  19. 462
  20. 450
  21. 139
  22. 339
  23. 3
  24. 5
  25. 19
  26. 24
  27. 18
  28. 5
  29. 7
  30. 5
  31. 115
  32. 3
  33. 14
  34. 576
  35. 113
  36. 6
  37. 516
  38. 19
  39. 456
  40. 30

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