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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 765 · 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 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 115 (c) 124 (d) 106
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  4. 4.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) 54 (c) 6 (d) 18
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 5 (d) 3
  6. 6.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 207 (c) 69 (d) 72
  7. 7.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) 12 (c) 108 (d) 36
  8. 8.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 5 (d) 4
  10. 10.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 420 (c) 430 (d) 358
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  13. 13.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 432 (d) 433
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 19 (d) 9
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  16. 16.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
  17. 17.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 450 (c) 372 (d) 441
  18. 18.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) 153 (b) 54 (c) 51 (d) 17
  19. 19.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 237 (c) 238 (d) 228
  20. 20.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) 27 (c) 81 (d) 9
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  22. 22.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) 18 (b) 5 (c) 15 (d) 45
  23. 23.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) 135 (c) 15 (d) 48
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 15 (d) 17
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 7 (b) 9 (c) 6 (d) 8
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 8 (b) 7 (c) 5 (d) 6
  28. 28.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 537 (c) 547 (d) 546
  29. 29.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 50 (d) 41
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
  31. 31.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 444 (c) 454 (d) 453
  32. 32.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 553 (c) 543 (d) 552
  33. 33.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 568 (c) 567 (d) 558
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  35. 35.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) 20 (b) 180 (c) 63 (d) 60
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 3 (d) 2
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 17 (b) 8 (c) 18 (d) 19
  38. 38.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) 14 (c) 42 (d) 126
  39. 39.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  40. 40.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) 33 (d) 99

Answer key

  1. 115
  2. 15
  3. 9
  4. 18
  5. 4
  6. 69
  7. 36
  8. 3
  9. 4
  10. 429
  11. 5
  12. 4
  13. 432
  14. 20
  15. 3
  16. 63
  17. 450
  18. 51
  19. 237
  20. 27
  21. 9
  22. 15
  23. 45
  24. 16
  25. 7
  26. 8
  27. 7
  28. 546
  29. 41
  30. 14
  31. 453
  32. 552
  33. 567
  34. 7
  35. 60
  36. 4
  37. 18
  38. 42
  39. 6
  40. 33

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