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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 541 · 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 7 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 3 (d) 2
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  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) 15 (b) 18 (c) 5 (d) 45
  7. 7.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) 126 (d) 45
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  10. 10.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) 51 (b) 17 (c) 54 (d) 153
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 7 (b) 6 (c) 8 (d) 9
  12. 12.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 466 (c) 456 (d) 382
  13. 13.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 59 (c) 50 (d) 68
  14. 14.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 320 (c) 373 (d) 372
  15. 15.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) 69 (c) 22 (d) 66
  16. 16.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) 27 (c) 30 (d) 81
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 11 (b) 10 (c) 8 (d) 9
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 12 (b) 7 (c) 14 (d) 15
  21. 21.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 408 (c) 505 (d) 504
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 19 (d) 20
  23. 23.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 196 (c) 187 (d) 188
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 16 (d) 6
  27. 27.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
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 14 (d) 4
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 18 (d) 17
  30. 30.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 504 (c) 414 (d) 513
  31. 31.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 207 (c) 208 (d) 198
  32. 32.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 439 (d) 438
  33. 33.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 118 (c) 110 (d) 109
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 4 (b) 7 (c) 6 (d) 5
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  37. 37.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 374 (c) 454 (d) 444
  38. 38.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 155 (d) 164
  39. 39.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
  40. 40.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 384 (c) 328 (d) 385

Answer key

  1. 4
  2. 19
  3. 6
  4. 9
  5. 2
  6. 15
  7. 42
  8. 7
  9. 9
  10. 51
  11. 8
  12. 465
  13. 59
  14. 372
  15. 66
  16. 27
  17. 3
  18. 2
  19. 10
  20. 14
  21. 504
  22. 19
  23. 187
  24. 5
  25. 3
  26. 17
  27. 24
  28. 15
  29. 18
  30. 513
  31. 207
  32. 438
  33. 109
  34. 6
  35. 5
  36. 5
  37. 453
  38. 155
  39. 21
  40. 384

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