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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 573 · 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.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 170 (c) 152 (d) 161
  2. 2.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 544 (c) 434 (d) 534
  3. 3.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) 36 (c) 108 (d) 39
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 17 (d) 16
  6. 6.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 60 (d) 78
  7. 7.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) 22 (b) 69 (c) 198 (d) 66
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 18 (d) 9
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15
  10. 10.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) 45 (b) 15 (c) 135 (d) 48
  11. 11.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) 33 (b) 11 (c) 99 (d) 36
  12. 12.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) 27 (b) 9 (c) 81 (d) 30
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 1 (d) 2
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  15. 15.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 219 (c) 220 (d) 218
  16. 16.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 108 (c) 99 (d) 90
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  18. 18.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 432 (c) 541 (d) 540
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 17 (d) 15
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 11 (b) 12 (c) 3 (d) 10
  22. 22.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) 17 (b) 153 (c) 51 (d) 54
  23. 23.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) 24 (b) 75 (c) 72 (d) 216
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 17 (c) 15 (d) 5
  25. 25.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 83 (c) 84 (d) 92
  26. 26.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
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 12 (c) 14 (d) 13
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 20 (d) 21
  31. 31.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
  32. 32.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 499 (d) 489
  33. 33.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  34. 34.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 339 (c) 340 (d) 330
  35. 35.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 483 (c) 492 (d) 493
  36. 36.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) 45 (c) 14 (d) 126
  37. 37.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 529 (c) 519 (d) 424
  38. 38.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 577 (c) 576 (d) 456
  39. 39.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 356 (c) 426 (d) 427
  40. 40.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 43 (c) 34 (d) 52

Answer key

  1. 161
  2. 543
  3. 36
  4. 2
  5. 17
  6. 69
  7. 66
  8. 19
  9. 15
  10. 45
  11. 33
  12. 27
  13. 3
  14. 3
  15. 219
  16. 99
  17. 6
  18. 540
  19. 16
  20. 8
  21. 11
  22. 51
  23. 72
  24. 16
  25. 83
  26. 471
  27. 4
  28. 6
  29. 13
  30. 20
  31. 63
  32. 498
  33. 4
  34. 339
  35. 492
  36. 42
  37. 528
  38. 576
  39. 426
  40. 43

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