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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 435 · 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 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) 180 (b) 63 (c) 20 (d) 60
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 5 (d) 4
  3. 3.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 627 (c) 490 (d) 618
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 4 (d) 3
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  6. 6.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) 445 (c) 444 (d) 368
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  9. 9.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) 6 (c) 21 (d) 18
  10. 10.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) 23 (b) 69 (c) 72 (d) 207
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 9 (c) 6 (d) 7
  12. 12.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 46 (c) 54 (d) 36
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  14. 14.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) 15 (b) 45 (c) 48 (d) 135
  15. 15.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) 63 (d) 66
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 3 (d) 4
  17. 17.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) 171 (c) 60 (d) 19
  18. 18.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) 298 (c) 297 (d) 288
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  23. 23.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) 33 (d) 10
  24. 24.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
  25. 25.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 183 (c) 193 (d) 192
  26. 26.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 595 (c) 594 (d) 585
  27. 27.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 580 (d) 579
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 6 (d) 4
  29. 29.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 348 (c) 415 (d) 414
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  31. 31.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 130 (c) 122 (d) 121
  32. 32.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) 63 (d) 24
  33. 33.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 291 (c) 282 (d) 266
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 16
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  37. 37.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) 16 (c) 144 (d) 48
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 3 (c) 9 (d) 8
  40. 40.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 498 (c) 499 (d) 404

Answer key

  1. 60
  2. 5
  3. 627
  4. 4
  5. 3
  6. 444
  7. 9
  8. 5
  9. 18
  10. 69
  11. 8
  12. 45
  13. 5
  14. 45
  15. 63
  16. 5
  17. 57
  18. 297
  19. 18
  20. 19
  21. 3
  22. 7
  23. 30
  24. 567
  25. 192
  26. 594
  27. 579
  28. 5
  29. 414
  30. 2
  31. 121
  32. 21
  33. 291
  34. 6
  35. 15
  36. 19
  37. 48
  38. 4
  39. 9
  40. 498

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