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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 873 · 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) 10 (b) 5 (c) 4 (d) 3
  2. 2.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 132 (d) 114
  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) 30 (b) 9 (c) 27 (d) 81
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  5. 5.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) 486 (c) 402 (d) 495
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  7. 7.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 94 (d) 86
  8. 8.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) 20 (b) 63 (c) 60 (d) 180
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 16 (c) 6 (d) 17
  10. 10.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) 63 (b) 21 (c) 7 (d) 24
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 17 (d) 19
  12. 12.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 22 (c) 32 (d) 31
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 8 (d) 18
  14. 14.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 130 (d) 129
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  16. 16.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) 224 (c) 228 (d) 229
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 16 (d) 7
  18. 18.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) 57 (b) 162 (c) 18 (d) 54
  19. 19.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 199 (c) 198 (d) 189
  20. 20.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 33 (d) 11
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 21
  22. 22.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 615 (c) 482 (d) 606
  23. 23.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 531 (c) 532 (d) 426
  24. 24.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 439 (b) 429 (c) 438 (d) 364
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  26. 26.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 471 (c) 480 (d) 481
  27. 27.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
  28. 28.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 35 (c) 44 (d) 26
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 9 (d) 20
  30. 30.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 292 (c) 331 (d) 321
  31. 31.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) 24 (b) 72 (c) 75 (d) 216
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 17 (d) 16
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 1 (d) 2
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 8 (b) 17 (c) 18 (d) 19
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 6 (b) 5 (c) 8 (d) 7
  36. 36.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) 66 (b) 21 (c) 189 (d) 63
  37. 37.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 213 (c) 223 (d) 222
  38. 38.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) 126 (b) 42 (c) 14 (d) 45
  39. 39.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  40. 40.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) 171 (c) 57 (d) 60

Answer key

  1. 4
  2. 123
  3. 27
  4. 5
  5. 495
  6. 18
  7. 85
  8. 60
  9. 17
  10. 21
  11. 18
  12. 31
  13. 19
  14. 129
  15. 7
  16. 228
  17. 17
  18. 54
  19. 198
  20. 33
  21. 20
  22. 615
  23. 531
  24. 438
  25. 18
  26. 480
  27. 18
  28. 35
  29. 19
  30. 330
  31. 72
  32. 17
  33. 3
  34. 18
  35. 7
  36. 63
  37. 222
  38. 42
  39. 6
  40. 57

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