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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 264 · 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 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) 108 (d) 36
  2. 2.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) 7 (d) 21
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 14 (b) 17 (c) 16 (d) 9
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 5 (d) 2
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 8 (b) 13 (c) 16 (d) 15
  6. 6.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) 207 (b) 72 (c) 23 (d) 69
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  8. 8.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) 18 (c) 45 (d) 15
  9. 9.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 52 (d) 61
  10. 10.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 288 (d) 324
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  12. 12.The numbers 4 to 12 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) 27 (c) 8 (d) 24
  13. 13.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 14 (b) 5 (c) 16 (d) 15
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  21. 21.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) 69 (b) 198 (c) 22 (d) 66
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 17 (b) 8 (c) 19 (d) 18
  23. 23.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 355 (c) 345 (d) 308
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
  26. 26.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) 45 (c) 42 (d) 14
  27. 27.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 118 (c) 128 (d) 127
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 9 (b) 8 (c) 3 (d) 10
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  30. 30.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 198 (c) 204 (d) 199
  31. 31.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) 60 (b) 63 (c) 20 (d) 180
  32. 32.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 399 (c) 409 (d) 408
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 5
  34. 34.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 459 (c) 469 (d) 384
  35. 35.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
  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) 30 (b) 9 (c) 81 (d) 27
  37. 37.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 360 (c) 369 (d) 370
  38. 38.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 573 (c) 583 (d) 582
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9

Answer key

  1. 36
  2. 21
  3. 16
  4. 4
  5. 15
  6. 69
  7. 2
  8. 15
  9. 61
  10. 324
  11. 8
  12. 24
  13. 5
  14. 9
  15. 8
  16. 3
  17. 6
  18. 18
  19. 15
  20. 4
  21. 66
  22. 18
  23. 354
  24. 3
  25. 18
  26. 42
  27. 127
  28. 9
  29. 4
  30. 198
  31. 60
  32. 408
  33. 4
  34. 468
  35. 33
  36. 27
  37. 369
  38. 582
  39. 5
  40. 20

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