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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 26 · 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 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
  2. 2.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 35 (d) 26
  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) 117 (b) 39 (c) 13 (d) 42
  4. 4.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 489 (c) 480 (d) 490
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 5 (d) 3
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 18 (d) 17
  9. 9.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) 33 (d) 30
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  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) 301 (b) 291 (c) 300 (d) 272
  13. 13.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 200 (d) 183
  14. 14.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 173 (c) 164 (d) 182
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 2 (d) 4
  16. 16.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) 66 (b) 21 (c) 189 (d) 63
  17. 17.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 72 (c) 54 (d) 63
  18. 18.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 546 (d) 537
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 19 (d) 17
  20. 20.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 292 (c) 266 (d) 282
  21. 21.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) 9 (b) 81 (c) 30 (d) 27
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  23. 23.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) 27 (c) 8 (d) 72
  24. 24.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) 126 (b) 14 (c) 45 (d) 42
  25. 25.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 334 (c) 393 (d) 384
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 4 (d) 14
  27. 27.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 297 (c) 306 (d) 307
  28. 28.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 444 (c) 368 (d) 445
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 19 (d) 8
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 9 (c) 3 (d) 10
  31. 31.The numbers 15 to 23 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) 60 (c) 19 (d) 171
  32. 32.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) 22 (c) 66 (d) 198
  33. 33.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) 5 (c) 18 (d) 15
  34. 34.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 358 (c) 357 (d) 310
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  36. 36.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 90 (c) 99 (d) 108
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
  38. 38.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 568 (c) 450 (d) 558
  39. 39.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 180 (c) 190 (d) 198
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 16 (d) 17

Answer key

  1. 21
  2. 35
  3. 39
  4. 489
  5. 3
  6. 6
  7. 5
  8. 17
  9. 30
  10. 7
  11. 18
  12. 300
  13. 192
  14. 173
  15. 4
  16. 63
  17. 63
  18. 546
  19. 18
  20. 291
  21. 27
  22. 9
  23. 24
  24. 42
  25. 393
  26. 15
  27. 306
  28. 444
  29. 19
  30. 9
  31. 57
  32. 66
  33. 15
  34. 357
  35. 8
  36. 99
  37. 18
  38. 567
  39. 189
  40. 16

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