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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 768 · 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 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) 36 (c) 99 (d) 33
  2. 2.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 122 (c) 121 (d) 112
  3. 3.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 568 (c) 567 (d) 450
  4. 4.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) 162 (d) 54
  5. 5.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) 21 (c) 18 (d) 54
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 19 (d) 18
  7. 7.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) 126 (c) 14 (d) 42
  8. 8.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) 480 (d) 398
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  11. 11.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 363 (c) 320 (d) 372
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 21 (d) 20
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 20 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  15. 15.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) 144 (c) 48 (d) 51
  16. 16.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 492 (c) 501 (d) 502
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 18 (d) 17
  18. 18.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 616 (c) 482 (d) 606
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 3 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  22. 22.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 477 (c) 390 (d) 468
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 3 (c) 4 (d) 5
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 19 (d) 9
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 6 (d) 3
  31. 31.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
  32. 32.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 120 (c) 128 (d) 119
  33. 33.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) 57 (d) 171
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 5 (d) 15
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 16 (d) 15
  36. 36.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 615 (c) 624 (d) 488
  37. 37.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) 36 (d) 108
  38. 38.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 206 (c) 192 (d) 202
  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) 216 (b) 72 (c) 75 (d) 24
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4

Answer key

  1. 33
  2. 121
  3. 567
  4. 54
  5. 18
  6. 18
  7. 42
  8. 489
  9. 6
  10. 5
  11. 372
  12. 20
  13. 19
  14. 2
  15. 48
  16. 501
  17. 18
  18. 615
  19. 5
  20. 5
  21. 3
  22. 477
  23. 4
  24. 8
  25. 16
  26. 9
  27. 8
  28. 5
  29. 19
  30. 5
  31. 300
  32. 119
  33. 57
  34. 16
  35. 15
  36. 624
  37. 36
  38. 201
  39. 72
  40. 4

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