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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 236 · 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 times is the digit 5 written when you write all the numbers from 1 to 35? (a) 4 (b) 5 (c) 2 (d) 3
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 12 (b) 5 (c) 14 (d) 13
  3. 3.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 232 (c) 231 (d) 241
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 3 (d) 4
  5. 5.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 196 (c) 178 (d) 188
  6. 6.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) 81 (b) 27 (c) 30 (d) 9
  7. 7.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) 15 (b) 18 (c) 45 (d) 5
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 19 (d) 17
  10. 10.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) 11 (d) 36
  11. 11.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 185 (c) 194 (d) 176
  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) 24 (c) 27 (d) 8
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 4 (c) 6 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  15. 15.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 336 (c) 327 (d) 337
  16. 16.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) 21 (c) 63 (d) 7
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  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) 30 (b) 10 (c) 33 (d) 90
  19. 19.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) 22 (c) 69 (d) 198
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  21. 21.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
  22. 22.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 208 (c) 205 (d) 204
  23. 23.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) 21 (b) 18 (c) 54 (d) 6
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  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) 481 (b) 471 (c) 480 (d) 392
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 5 (b) 7 (c) 6 (d) 4
  28. 28.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 144 (d) 48
  29. 29.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) 42 (b) 126 (c) 14 (d) 45
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
  31. 31.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 441 (c) 451 (d) 372
  32. 32.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) 39 (b) 12 (c) 108 (d) 36
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 9 (b) 10 (c) 8 (d) 3
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  35. 35.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 519 (c) 529 (d) 528
  36. 36.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 549 (c) 438 (d) 540
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  38. 38.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) 180 (b) 60 (c) 20 (d) 63
  39. 39.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 618 (d) 619
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 3 (b) 4 (c) 5 (d) 6

Answer key

  1. 4
  2. 13
  3. 240
  4. 5
  5. 187
  6. 27
  7. 15
  8. 19
  9. 18
  10. 33
  11. 185
  12. 24
  13. 6
  14. 6
  15. 336
  16. 21
  17. 7
  18. 30
  19. 66
  20. 8
  21. 72
  22. 204
  23. 18
  24. 3
  25. 5
  26. 480
  27. 6
  28. 48
  29. 42
  30. 3
  31. 450
  32. 36
  33. 9
  34. 3
  35. 528
  36. 549
  37. 8
  38. 60
  39. 618
  40. 5

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