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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 530 · 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.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  2. 2.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) 7 (b) 63 (c) 24 (d) 21
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 4 (d) 14
  4. 4.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 70 (c) 69 (d) 78
  5. 5.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) 66 (b) 198 (c) 22 (d) 69
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 17 (c) 6 (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) 42 (b) 126 (c) 45 (d) 14
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 4 (b) 5 (c) 6 (d) 3
  9. 9.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 222 (c) 223 (d) 213
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 13 (d) 14
  12. 12.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 72 (c) 63 (d) 64
  13. 13.The numbers 16 to 24 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) 180 (c) 20 (d) 60
  14. 14.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 422 (c) 525 (d) 526
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  18. 18.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 282 (c) 316 (d) 306
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 7 (b) 8 (c) 5 (d) 6
  20. 20.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) 21 (b) 18 (c) 54 (d) 6
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 7 (b) 17 (c) 18 (d) 19
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 2 (b) 1 (c) 4 (d) 3
  23. 23.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) 36 (b) 108 (c) 12 (d) 39
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 3 (b) 2 (c) 4 (d) 5
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 14 (b) 16 (c) 5 (d) 15
  27. 27.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 382 (c) 466 (d) 465
  28. 28.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  29. 29.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 454 (c) 374 (d) 444
  30. 30.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 630 (c) 639 (d) 498
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 20 (b) 21 (c) 9 (d) 19
  32. 32.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 598 (c) 470 (d) 588
  33. 33.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  34. 34.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 153 (d) 144
  35. 35.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 300 (c) 343 (d) 342
  36. 36.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) 30 (b) 33 (c) 90 (d) 10
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 17 (d) 6
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 17 (c) 16 (d) 15
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  40. 40.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 202 (c) 195 (d) 196

Answer key

  1. 8
  2. 21
  3. 15
  4. 69
  5. 66
  6. 17
  7. 42
  8. 5
  9. 222
  10. 3
  11. 14
  12. 63
  13. 60
  14. 525
  15. 3
  16. 8
  17. 4
  18. 315
  19. 7
  20. 18
  21. 18
  22. 3
  23. 36
  24. 3
  25. 4
  26. 15
  27. 465
  28. 7
  29. 453
  30. 639
  31. 20
  32. 597
  33. 4
  34. 153
  35. 342
  36. 30
  37. 17
  38. 16
  39. 5
  40. 195

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