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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 317 · 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 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) 24 (c) 21 (d) 7
  2. 2.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) 45 (b) 5 (c) 18 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  4. 4.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) 66 (b) 69 (c) 198 (d) 22
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 1 (d) 3
  9. 9.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 303 (c) 313 (d) 312
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 5 (d) 4
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 6 (b) 7 (c) 4 (d) 5
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 1 (d) 3
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  16. 16.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 348 (c) 415 (d) 405
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 14 (d) 15
  18. 18.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 624 (c) 494 (d) 633
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  20. 20.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) 406 (d) 501
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  22. 22.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 601 (c) 591 (d) 600
  23. 23.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 434 (c) 543 (d) 534
  24. 24.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) 207 (c) 72 (d) 23
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  26. 26.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) 18 (d) 6
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 2 (d) 4
  28. 28.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) 438 (c) 429 (d) 364
  29. 29.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 143 (c) 134 (d) 152
  30. 30.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 300 (c) 333 (d) 343
  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) 75 (b) 216 (c) 24 (d) 72
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 7 (b) 4 (c) 6 (d) 5
  33. 33.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 84 (d) 75
  34. 34.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) 223 (c) 213 (d) 222
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  36. 36.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) 36 (b) 39 (c) 108 (d) 12
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 5 (d) 4
  38. 38.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  39. 39.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) 30 (b) 33 (c) 10 (d) 90
  40. 40.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 241 (c) 240 (d) 232

Answer key

  1. 21
  2. 15
  3. 5
  4. 66
  5. 8
  6. 9
  7. 4
  8. 3
  9. 312
  10. 6
  11. 7
  12. 5
  13. 6
  14. 3
  15. 19
  16. 414
  17. 14
  18. 633
  19. 9
  20. 501
  21. 7
  22. 600
  23. 543
  24. 69
  25. 2
  26. 18
  27. 4
  28. 438
  29. 143
  30. 342
  31. 72
  32. 6
  33. 75
  34. 222
  35. 4
  36. 36
  37. 4
  38. 8
  39. 30
  40. 240

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