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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 697 · 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 9 written when you write all the numbers from 1 to 87? (a) 8 (b) 7 (c) 9 (d) 6
  2. 2.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 230 (c) 237 (d) 228
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 7 (b) 4 (c) 5 (d) 6
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 7 (b) 10 (c) 8 (d) 9
  5. 5.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 28 (c) 46 (d) 37
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  7. 7.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 358 (c) 310 (d) 357
  8. 8.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) 108 (b) 39 (c) 36 (d) 12
  9. 9.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) 8 (b) 72 (c) 27 (d) 24
  10. 10.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) 6 (b) 18 (c) 21 (d) 54
  11. 11.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 253 (d) 252
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  15. 15.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 42 (c) 24 (d) 34
  16. 16.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 136 (c) 118 (d) 128
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 5 (c) 3 (d) 4
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 14 (d) 15
  19. 19.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 486 (c) 477 (d) 396
  20. 20.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) 171 (b) 57 (c) 60 (d) 19
  21. 21.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 484 (c) 619 (d) 618
  22. 22.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) 45 (b) 14 (c) 42 (d) 126
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 2 (d) 3
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 6 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  26. 26.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 451 (c) 450 (d) 372
  27. 27.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 427 (c) 356 (d) 417
  28. 28.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 546 (c) 555 (d) 442
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 15 (d) 17
  30. 30.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) 72 (c) 23 (d) 207
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 13 (b) 3 (c) 14 (d) 12
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 18 (d) 16
  34. 34.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  35. 35.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 380 (c) 462 (d) 453
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  39. 39.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) 72 (b) 24 (c) 75 (d) 216
  40. 40.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) 99 (c) 33 (d) 36

Answer key

  1. 8
  2. 237
  3. 6
  4. 9
  5. 37
  6. 5
  7. 357
  8. 36
  9. 24
  10. 18
  11. 252
  12. 7
  13. 3
  14. 3
  15. 33
  16. 127
  17. 4
  18. 14
  19. 486
  20. 57
  21. 618
  22. 42
  23. 3
  24. 5
  25. 5
  26. 450
  27. 426
  28. 555
  29. 16
  30. 69
  31. 13
  32. 8
  33. 17
  34. 8
  35. 462
  36. 4
  37. 4
  38. 17
  39. 72
  40. 33

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