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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 482 · 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 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) 39 (c) 108 (d) 36
  2. 2.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) 19 (b) 60 (c) 171 (d) 57
  3. 3.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) 24 (c) 27 (d) 8
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 7 (b) 9 (c) 8 (d) 6
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 6 (d) 4
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 5 (b) 16 (c) 17 (d) 15
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  9. 9.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 388 (c) 330 (d) 387
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 20 (b) 19 (c) 18 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 3 (d) 15
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  15. 15.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 420 (c) 411 (d) 352
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  17. 17.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) 69 (b) 22 (c) 66 (d) 198
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  20. 20.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) 189 (b) 21 (c) 66 (d) 63
  21. 21.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) 30 (b) 81 (c) 27 (d) 9
  22. 22.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 172 (d) 163
  23. 23.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 480 (c) 613 (d) 603
  24. 24.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 582 (d) 466
  25. 25.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) 15 (c) 18 (d) 5
  26. 26.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 135 (d) 136
  27. 27.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 37 (c) 38 (d) 46
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 18 (c) 17 (d) 6
  29. 29.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) 382 (c) 466 (d) 456
  30. 30.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 642 (c) 643 (d) 633
  31. 31.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) 57 (b) 18 (c) 54 (d) 162
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 6 (b) 8 (c) 7 (d) 9
  33. 33.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) 126 (c) 14 (d) 45
  34. 34.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 492 (c) 493 (d) 400
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 15 (c) 16 (d) 14
  36. 36.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 138 (c) 147 (d) 156
  37. 37.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
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
  39. 39.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 247 (c) 246 (d) 237
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10

Answer key

  1. 36
  2. 57
  3. 24
  4. 8
  5. 5
  6. 16
  7. 2
  8. 4
  9. 387
  10. 19
  11. 9
  12. 6
  13. 14
  14. 20
  15. 420
  16. 3
  17. 66
  18. 4
  19. 2
  20. 63
  21. 27
  22. 163
  23. 612
  24. 591
  25. 15
  26. 135
  27. 37
  28. 17
  29. 465
  30. 642
  31. 54
  32. 8
  33. 42
  34. 492
  35. 15
  36. 147
  37. 10
  38. 4
  39. 246
  40. 7

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