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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 663 · 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 11? (a) 8 (b) 12 (c) 9 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  3. 3.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 543 (c) 440 (d) 553
  4. 4.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 216 (d) 217
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 13 (d) 12
  6. 6.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) 5 (c) 45 (d) 15
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  8. 8.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 46 (d) 28
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 11 (b) 10 (c) 8 (d) 9
  10. 10.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) 126 (c) 42 (d) 45
  11. 11.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 61 (c) 62 (d) 52
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  13. 13.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 64 (c) 74 (d) 73
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  15. 15.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) 13 (c) 42 (d) 39
  16. 16.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 406 (c) 342 (d) 396
  17. 17.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 65 (d) 56
  18. 18.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) 90 (c) 33 (d) 30
  19. 19.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 48 (c) 38 (d) 47
  20. 20.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) 63 (c) 7 (d) 24
  21. 21.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 125 (c) 134 (d) 116
  22. 22.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) 21 (c) 6 (d) 18
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 6 (c) 7 (d) 5
  24. 24.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 204 (c) 214 (d) 213
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 7 (d) 8
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 2 (d) 3
  27. 27.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 390 (d) 338
  28. 28.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 213 (d) 222
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 5 (d) 3
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 16 (d) 14
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  34. 34.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) 99 (b) 33 (c) 36 (d) 11
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  36. 36.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 375 (c) 385 (d) 328
  37. 37.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 300 (d) 343
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 1 (d) 3
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  40. 40.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 277 (c) 276 (d) 256

Answer key

  1. 8
  2. 4
  3. 552
  4. 216
  5. 13
  6. 15
  7. 6
  8. 37
  9. 10
  10. 42
  11. 61
  12. 19
  13. 73
  14. 5
  15. 39
  16. 405
  17. 65
  18. 30
  19. 47
  20. 21
  21. 125
  22. 18
  23. 7
  24. 213
  25. 7
  26. 3
  27. 399
  28. 222
  29. 5
  30. 4
  31. 7
  32. 15
  33. 6
  34. 33
  35. 4
  36. 384
  37. 342
  38. 3
  39. 16
  40. 276

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