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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 437 · 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.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 344 (c) 408 (d) 399
  2. 2.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) 54 (b) 57 (c) 18 (d) 162
  3. 3.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) 481 (c) 471 (d) 392
  4. 4.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 558 (c) 568 (d) 567
  5. 5.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 264 (d) 274
  6. 6.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) 33 (b) 11 (c) 36 (d) 99
  7. 7.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 330 (c) 331 (d) 292
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  11. 11.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) 45 (d) 48
  12. 12.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) 170 (c) 179 (d) 180
  13. 13.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) 35 (c) 44 (d) 36
  14. 14.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) 5 (b) 15 (c) 45 (d) 18
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 4 (d) 6
  16. 16.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 336 (c) 387 (d) 397
  17. 17.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) 307 (c) 297 (d) 306
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 13 (b) 11 (c) 7 (d) 14
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 16 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  23. 23.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) 490 (c) 480 (d) 489
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  28. 28.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 146 (c) 137 (d) 138
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 5 (b) 4 (c) 6 (d) 7
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 6 (b) 8 (c) 7 (d) 5
  33. 33.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) 51 (b) 144 (c) 16 (d) 48
  34. 34.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 346 (d) 302
  35. 35.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 360 (c) 312 (d) 361
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 5 (d) 16
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 4 (c) 6 (d) 7
  38. 38.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 458 (d) 579
  39. 39.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) 39 (c) 13 (d) 117
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6

Answer key

  1. 408
  2. 54
  3. 480
  4. 567
  5. 273
  6. 33
  7. 330
  8. 7
  9. 3
  10. 8
  11. 45
  12. 179
  13. 35
  14. 15
  15. 5
  16. 396
  17. 306
  18. 4
  19. 9
  20. 13
  21. 17
  22. 4
  23. 489
  24. 2
  25. 7
  26. 4
  27. 3
  28. 137
  29. 16
  30. 6
  31. 2
  32. 7
  33. 48
  34. 345
  35. 360
  36. 16
  37. 6
  38. 579
  39. 39
  40. 5

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