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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 883 · 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 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) 18 (c) 15 (d) 45
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 18 (d) 20
  3. 3.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) 69 (b) 72 (c) 23 (d) 207
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  5. 5.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 94 (d) 102
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 17
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 9 (b) 8 (c) 6 (d) 7
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 8 (c) 9 (d) 7
  11. 11.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 12 (c) 14 (d) 13
  13. 13.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 328 (c) 384 (d) 385
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 15 (d) 5
  15. 15.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 108 (d) 107
  16. 16.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) 171 (b) 19 (c) 60 (d) 57
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 4 (d) 1
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  20. 20.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) 162 (b) 18 (c) 57 (d) 54
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 17 (d) 19
  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) 10 (b) 30 (c) 33 (d) 90
  24. 24.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 619 (d) 618
  25. 25.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 501 (d) 406
  26. 26.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 122 (c) 132 (d) 131
  27. 27.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) 51 (c) 16 (d) 48
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 17 (b) 6 (c) 16 (d) 18
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 8 (d) 18
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 12 (b) 8 (c) 14 (d) 15
  32. 32.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 517 (c) 507 (d) 516
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 5 (d) 17
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 9 (d) 19
  35. 35.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 482 (b) 615 (c) 606 (d) 616
  36. 36.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) 45 (c) 42 (d) 126
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15

Answer key

  1. 15
  2. 19
  3. 69
  4. 8
  5. 93
  6. 18
  7. 6
  8. 3
  9. 8
  10. 8
  11. 600
  12. 13
  13. 384
  14. 15
  15. 107
  16. 57
  17. 3
  18. 19
  19. 20
  20. 54
  21. 2
  22. 18
  23. 30
  24. 618
  25. 501
  26. 131
  27. 48
  28. 17
  29. 19
  30. 4
  31. 14
  32. 516
  33. 16
  34. 19
  35. 615
  36. 42
  37. 6
  38. 2
  39. 9
  40. 5

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