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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 812 · 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 2? (a) 2 (b) 10 (c) 1 (d) 3
  2. 2.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 354 (c) 414 (d) 424
  3. 3.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 531 (c) 532 (d) 522
  4. 4.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
  5. 5.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 315 (c) 325 (d) 324
  6. 6.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 477 (d) 478
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 13 (d) 3
  14. 14.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 432 (c) 360 (d) 433
  15. 15.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) 18 (b) 54 (c) 162 (d) 57
  16. 16.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 381 (c) 332 (d) 391
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 9 (c) 6 (d) 7
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 19 (d) 8
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  21. 21.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 549 (c) 558 (d) 444
  22. 22.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) 66 (b) 22 (c) 69 (d) 198
  23. 23.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) 216 (b) 24 (c) 75 (d) 72
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 4 (b) 6 (c) 7 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 17 (b) 6 (c) 15 (d) 16
  26. 26.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) 33 (b) 90 (c) 10 (d) 30
  27. 27.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 270 (c) 279 (d) 258
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 18 (b) 17 (c) 19 (d) 8
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 3 (b) 4 (c) 6 (d) 5
  30. 30.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 495 (c) 486 (d) 402
  31. 31.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 585 (c) 468 (d) 595
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 7 (d) 16
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 20 (d) 18
  34. 34.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 100 (c) 92 (d) 91
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 16 (d) 18
  36. 36.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) 39 (b) 42 (c) 13 (d) 117
  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) 144 (c) 48 (d) 16
  38. 38.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) 18 (b) 15 (c) 45 (d) 5
  39. 39.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19

Answer key

  1. 2
  2. 423
  3. 531
  4. 18
  5. 324
  6. 477
  7. 9
  8. 4
  9. 4
  10. 8
  11. 5
  12. 2
  13. 14
  14. 432
  15. 54
  16. 390
  17. 8
  18. 19
  19. 19
  20. 19
  21. 558
  22. 66
  23. 72
  24. 6
  25. 16
  26. 30
  27. 279
  28. 18
  29. 5
  30. 495
  31. 594
  32. 17
  33. 19
  34. 91
  35. 17
  36. 39
  37. 48
  38. 15
  39. 7
  40. 19

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