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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 460 · 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 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) 207 (b) 23 (c) 69 (d) 72
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  4. 4.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 642 (c) 500 (d) 633
  5. 5.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 164 (d) 155
  6. 6.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
  7. 7.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) 399 (d) 408
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
  9. 9.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 286 (d) 322
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  11. 11.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) 14 (b) 42 (c) 45 (d) 126
  12. 12.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) 30 (b) 90 (c) 10 (d) 33
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 4 (c) 5 (d) 2
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 3 (c) 9 (d) 10
  16. 16.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 501 (c) 510 (d) 511
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 6 (c) 8 (d) 7
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 15 (d) 17
  19. 19.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) 16 (c) 51 (d) 48
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 6 (c) 4 (d) 5
  23. 23.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 351 (d) 243
  24. 24.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) 18 (b) 6 (c) 21 (d) 54
  25. 25.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
  26. 26.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
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 17 (d) 18
  28. 28.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 392 (c) 480 (d) 471
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 5 (b) 7 (c) 6 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 6 (d) 5
  32. 32.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 128 (c) 120 (d) 119
  33. 33.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) 7 (b) 63 (c) 21 (d) 24
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 20 (d) 9
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 12 (b) 5 (c) 14 (d) 13
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 16 (d) 7
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 16 (b) 17 (c) 15 (d) 6
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 16 (d) 18
  40. 40.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 505 (c) 408 (d) 504

Answer key

  1. 69
  2. 4
  3. 8
  4. 642
  5. 155
  6. 27
  7. 408
  8. 20
  9. 321
  10. 5
  11. 42
  12. 30
  13. 4
  14. 9
  15. 10
  16. 510
  17. 7
  18. 16
  19. 48
  20. 2
  21. 6
  22. 6
  23. 243
  24. 18
  25. 312
  26. 63
  27. 18
  28. 480
  29. 6
  30. 3
  31. 6
  32. 119
  33. 21
  34. 20
  35. 4
  36. 13
  37. 17
  38. 16
  39. 17
  40. 504

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