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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 600 · 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 8? (a) 8 (b) 10 (c) 7 (d) 9
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  3. 3.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 33 (d) 34
  4. 4.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 594 (c) 604 (d) 474
  5. 5.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 134 (d) 133
  6. 6.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) 42 (c) 45 (d) 126
  7. 7.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) 57 (b) 171 (c) 60 (d) 19
  8. 8.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) 22 (c) 69 (d) 66
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 2 (d) 1
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 17
  11. 11.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) 6 (c) 21 (d) 54
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 2 (d) 3
  13. 13.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 315 (c) 316 (d) 306
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 2 (d) 5
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 4 (b) 7 (c) 6 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  17. 17.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 170 (c) 179 (d) 188
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 7 (b) 8 (c) 5 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  20. 20.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) 13 (b) 42 (c) 117 (d) 39
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 3 (d) 2
  22. 22.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 176 (c) 167 (d) 168
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 16 (b) 15 (c) 17 (d) 6
  24. 24.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) 75 (b) 72 (c) 24 (d) 216
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  26. 26.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 52 (c) 34 (d) 44
  27. 27.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) 24 (b) 7 (c) 21 (d) 63
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 7 (d) 16
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 13 (c) 14 (d) 15
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 16 (d) 17
  32. 32.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 453 (c) 454 (d) 374
  33. 33.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) 11 (b) 36 (c) 33 (d) 99
  34. 34.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 348 (c) 349 (d) 339
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 18
  36. 36.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) 9 (b) 30 (c) 81 (d) 27
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 5 (b) 4 (c) 6 (d) 3
  38. 38.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 54 (c) 51 (d) 17
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 5 (d) 3
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7

Answer key

  1. 8
  2. 2
  3. 33
  4. 603
  5. 133
  6. 42
  7. 57
  8. 66
  9. 3
  10. 18
  11. 18
  12. 4
  13. 315
  14. 4
  15. 6
  16. 4
  17. 179
  18. 7
  19. 3
  20. 39
  21. 4
  22. 167
  23. 16
  24. 72
  25. 7
  26. 43
  27. 21
  28. 18
  29. 17
  30. 14
  31. 16
  32. 453
  33. 33
  34. 348
  35. 19
  36. 27
  37. 5
  38. 51
  39. 5
  40. 7

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