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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 127 · 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 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) 16 (b) 48 (c) 51 (d) 144
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  3. 3.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) 45 (b) 18 (c) 5 (d) 15
  4. 4.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) 63 (b) 66 (c) 21 (d) 189
  5. 5.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 354 (c) 424 (d) 423
  6. 6.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) 7 (d) 63
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  8. 8.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
  9. 9.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) 33 (c) 99 (d) 36
  10. 10.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 162 (c) 161 (d) 170
  11. 11.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) 126 (b) 45 (c) 14 (d) 42
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  14. 14.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) 54 (c) 153 (d) 51
  15. 15.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) 57 (b) 19 (c) 171 (d) 60
  16. 16.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) 90 (b) 10 (c) 33 (d) 30
  17. 17.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 111 (c) 112 (d) 120
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 1 (b) 3 (c) 4 (d) 2
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  20. 20.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 505 (c) 408 (d) 495
  21. 21.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) 108 (c) 36 (d) 12
  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 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 597 (c) 607 (d) 606
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 4 (d) 16
  25. 25.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 84 (c) 75 (d) 66
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 16 (b) 17 (c) 14 (d) 8
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 18 (d) 8
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 17 (d) 16
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 9 (d) 19
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 17 (d) 5
  32. 32.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) 30 (c) 81 (d) 27
  33. 33.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 494 (c) 624 (d) 634
  34. 34.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 427 (d) 426
  35. 35.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) 462 (c) 472 (d) 471
  36. 36.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 95 (d) 96
  37. 37.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 489 (c) 398 (d) 480
  38. 38.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 77 (c) 68 (d) 78
  39. 39.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8

Answer key

  1. 48
  2. 9
  3. 15
  4. 63
  5. 423
  6. 21
  7. 3
  8. 72
  9. 33
  10. 161
  11. 42
  12. 2
  13. 6
  14. 51
  15. 57
  16. 30
  17. 111
  18. 3
  19. 9
  20. 504
  21. 36
  22. 19
  23. 606
  24. 15
  25. 75
  26. 16
  27. 19
  28. 16
  29. 8
  30. 19
  31. 16
  32. 27
  33. 633
  34. 426
  35. 471
  36. 95
  37. 489
  38. 77
  39. 3
  40. 7

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