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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 34 · 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 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) 18 (b) 162 (c) 54 (d) 57
  2. 2.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) 13 (c) 39 (d) 117
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  4. 4.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) 189 (c) 66 (d) 21
  5. 5.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) 60 (b) 63 (c) 20 (d) 180
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  7. 7.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 61 (c) 52 (d) 70
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 19 (d) 18
  9. 9.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) 27 (b) 72 (c) 24 (d) 8
  10. 10.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) 51 (c) 16 (d) 48
  11. 11.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) 21 (c) 7 (d) 63
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 5 (d) 2
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 13 (c) 14 (d) 15
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  15. 15.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 295 (c) 268 (d) 285
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  18. 18.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 125 (c) 116 (d) 126
  19. 19.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 256 (c) 242 (d) 255
  20. 20.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 367 (c) 316 (d) 366
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 18 (b) 20 (c) 8 (d) 19
  22. 22.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) 72 (b) 23 (c) 69 (d) 207
  23. 23.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 94 (c) 76 (d) 86
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 2
  25. 25.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 297 (c) 288 (d) 298
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 9 (d) 18
  27. 27.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 66 (c) 48 (d) 57
  28. 28.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 619 (d) 618
  29. 29.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 150 (c) 142 (d) 141
  30. 30.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 77 (b) 86 (c) 68 (d) 78
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 18 (d) 19
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 16 (d) 6
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 4 (d) 3
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 20 (d) 9
  36. 36.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 435 (c) 426 (d) 436
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 6 (c) 7 (d) 5
  38. 38.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 456 (d) 457
  39. 39.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 466 (c) 456 (d) 382
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 6 (d) 4

Answer key

  1. 54
  2. 39
  3. 2
  4. 63
  5. 60
  6. 5
  7. 61
  8. 18
  9. 24
  10. 48
  11. 21
  12. 4
  13. 14
  14. 9
  15. 294
  16. 3
  17. 4
  18. 125
  19. 255
  20. 366
  21. 19
  22. 69
  23. 85
  24. 4
  25. 297
  26. 19
  27. 57
  28. 618
  29. 141
  30. 77
  31. 6
  32. 19
  33. 17
  34. 3
  35. 19
  36. 435
  37. 7
  38. 456
  39. 465
  40. 5

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