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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 776 · 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 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
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 9 (c) 10 (d) 3
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
  4. 4.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 498 (c) 410 (d) 508
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 18 (b) 17 (c) 15 (d) 9
  7. 7.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 384 (c) 375 (d) 328
  8. 8.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 471 (c) 472 (d) 462
  9. 9.The numbers 11 to 19 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) 48 (c) 45 (d) 135
  10. 10.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
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 9 (d) 20
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 5 (d) 4
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5
  15. 15.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 237 (c) 236 (d) 247
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 16 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  18. 18.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 423 (c) 354 (d) 414
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 6 (b) 7 (c) 5 (d) 8
  20. 20.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) 153 (b) 54 (c) 17 (d) 51
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 18 (d) 20
  22. 22.The numbers 14 to 22 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) 57 (c) 162 (d) 18
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 2 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 14 (b) 15 (c) 16 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  28. 28.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) 24 (b) 8 (c) 27 (d) 72
  29. 29.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) 12 (c) 39 (d) 36
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 5 (d) 3
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 18 (b) 19 (c) 17 (d) 7
  32. 32.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 403 (c) 340 (d) 402
  33. 33.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 460 (c) 583 (d) 582
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 4 (d) 5
  35. 35.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) 6 (c) 21 (d) 18
  36. 36.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  37. 37.The numbers 17 to 25 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) 63 (c) 189 (d) 66
  38. 38.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  40. 40.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 606 (c) 482 (d) 615

Answer key

  1. 66
  2. 9
  3. 18
  4. 507
  5. 6
  6. 17
  7. 384
  8. 471
  9. 45
  10. 72
  11. 19
  12. 4
  13. 5
  14. 15
  15. 246
  16. 16
  17. 6
  18. 423
  19. 7
  20. 51
  21. 19
  22. 54
  23. 3
  24. 3
  25. 7
  26. 15
  27. 5
  28. 24
  29. 36
  30. 4
  31. 18
  32. 402
  33. 582
  34. 4
  35. 18
  36. 2
  37. 63
  38. 4
  39. 4
  40. 615

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