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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 146 · 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 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) 45 (d) 15
  2. 2.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) 207 (b) 69 (c) 72 (d) 23
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  4. 4.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 125 (c) 116 (d) 126
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 4 (b) 3 (c) 5 (d) 6
  6. 6.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) 216 (d) 75
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  8. 8.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) 78 (c) 68 (d) 77
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 7 (c) 17 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  13. 13.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) 33 (b) 90 (c) 10 (d) 30
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 16 (b) 15 (c) 4 (d) 14
  15. 15.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 540 (c) 550 (d) 549
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  18. 18.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) 36 (b) 33 (c) 99 (d) 11
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  20. 20.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 637 (c) 627 (d) 636
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  22. 22.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) 51 (c) 54 (d) 17
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 2 (d) 5
  25. 25.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) 60 (c) 180 (d) 63
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 11 (b) 10 (c) 3 (d) 12
  27. 27.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) 8 (b) 72 (c) 24 (d) 27
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 2 (d) 5
  31. 31.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) 69 (c) 78 (d) 70
  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) 553 (b) 543 (c) 552 (d) 440
  33. 33.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 314 (c) 354 (d) 363
  34. 34.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) 36 (d) 108
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  36. 36.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  37. 37.The numbers 9 to 17 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) 117 (c) 13 (d) 42
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  39. 39.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) 15 (b) 48 (c) 45 (d) 135
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 15 (d) 5

Answer key

  1. 15
  2. 69
  3. 17
  4. 125
  5. 5
  6. 72
  7. 9
  8. 77
  9. 17
  10. 6
  11. 4
  12. 4
  13. 30
  14. 15
  15. 549
  16. 4
  17. 3
  18. 33
  19. 9
  20. 636
  21. 7
  22. 51
  23. 8
  24. 4
  25. 60
  26. 11
  27. 24
  28. 2
  29. 20
  30. 4
  31. 69
  32. 552
  33. 363
  34. 36
  35. 17
  36. 41
  37. 39
  38. 16
  39. 45
  40. 16

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