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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 734 · 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 9? (a) 9 (b) 10 (c) 8 (d) 11
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 14 (b) 15 (c) 3 (d) 13
  3. 3.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) 81 (b) 30 (c) 27 (d) 9
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 10 (b) 9 (c) 11 (d) 8
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 17 (d) 6
  7. 7.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) 54 (c) 6 (d) 21
  8. 8.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) 42 (b) 45 (c) 14 (d) 126
  9. 9.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) 198 (b) 69 (c) 66 (d) 22
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 16 (b) 6 (c) 18 (d) 17
  11. 11.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 606 (c) 482 (d) 616
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  13. 13.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) 516 (c) 517 (d) 507
  14. 14.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 54 (c) 64 (d) 63
  15. 15.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 62 (d) 53
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 12 (b) 11 (c) 9 (d) 10
  18. 18.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 624 (c) 615 (d) 625
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  20. 20.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) 60 (c) 63 (d) 20
  21. 21.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 259 (d) 258
  22. 22.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) 135 (b) 45 (c) 15 (d) 48
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  24. 24.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 132 (c) 150 (d) 141
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  26. 26.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) 15 (c) 18 (d) 45
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 4 (d) 1
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21
  30. 30.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 64 (c) 46 (d) 55
  31. 31.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 229 (c) 228 (d) 224
  32. 32.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) 117 (b) 42 (c) 13 (d) 39
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 6 (b) 4 (c) 3 (d) 5
  34. 34.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 39 (c) 36 (d) 108
  35. 35.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 110 (d) 120
  36. 36.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 342 (c) 351 (d) 352
  37. 37.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) 72 (b) 23 (c) 207 (d) 69
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 5 (d) 3
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 5 (d) 4

Answer key

  1. 9
  2. 14
  3. 27
  4. 10
  5. 3
  6. 17
  7. 18
  8. 42
  9. 66
  10. 17
  11. 615
  12. 9
  13. 516
  14. 63
  15. 53
  16. 3
  17. 11
  18. 624
  19. 7
  20. 60
  21. 258
  22. 45
  23. 8
  24. 141
  25. 4
  26. 15
  27. 18
  28. 3
  29. 20
  30. 55
  31. 228
  32. 39
  33. 5
  34. 36
  35. 119
  36. 351
  37. 69
  38. 18
  39. 5
  40. 5

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