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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 540 · 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.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  2. 2.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 453 (c) 374 (d) 454
  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) 13 (b) 39 (c) 117 (d) 42
  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) 568 (b) 450 (c) 558 (d) 567
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 16 (d) 17
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 6 (d) 5
  7. 7.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) 21 (b) 7 (c) 24 (d) 63
  8. 8.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) 30 (c) 90 (d) 33
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  10. 10.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 98 (c) 106 (d) 88
  11. 11.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) 72 (b) 24 (c) 75 (d) 216
  12. 12.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 466 (c) 465 (d) 382
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 13 (c) 9 (d) 14
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  15. 15.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) 19 (b) 57 (c) 171 (d) 60
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 20 (d) 18
  17. 17.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 597 (c) 607 (d) 476
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 5 (b) 6 (c) 8 (d) 7
  21. 21.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 468 (c) 478 (d) 477
  22. 22.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 4 (d) 2
  25. 25.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 58 (d) 57
  26. 26.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) 48 (c) 144 (d) 16
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  28. 28.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 163 (d) 172
  29. 29.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 330 (c) 388 (d) 378
  30. 30.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 396 (c) 406 (d) 342
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 14 (b) 13 (c) 12 (d) 5
  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) 22 (b) 69 (c) 198 (d) 66
  33. 33.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) 18 (c) 21 (d) 6
  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) 346 (b) 336 (c) 302 (d) 345
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 13 (c) 15 (d) 14
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 6 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 5 (d) 3

Answer key

  1. 4
  2. 453
  3. 39
  4. 567
  5. 16
  6. 5
  7. 21
  8. 30
  9. 6
  10. 97
  11. 72
  12. 465
  13. 13
  14. 2
  15. 57
  16. 19
  17. 606
  18. 3
  19. 7
  20. 7
  21. 477
  22. 8
  23. 5
  24. 3
  25. 57
  26. 48
  27. 9
  28. 163
  29. 387
  30. 405
  31. 13
  32. 66
  33. 18
  34. 345
  35. 7
  36. 14
  37. 5
  38. 17
  39. 9
  40. 4

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