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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 416 · 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 times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 19 (d) 9
  2. 2.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) 90 (b) 30 (c) 33 (d) 10
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 17 (d) 19
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 3 (d) 5
  6. 6.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 103 (c) 94 (d) 104
  7. 7.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) 144 (b) 51 (c) 16 (d) 48
  8. 8.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 384 (c) 394 (d) 334
  9. 9.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) 24 (b) 8 (c) 72 (d) 27
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  11. 11.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) 81 (b) 30 (c) 27 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 7 (b) 10 (c) 13 (d) 12
  14. 14.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) 63 (b) 21 (c) 66 (d) 189
  15. 15.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) 54 (b) 21 (c) 6 (d) 18
  16. 16.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 91 (c) 100 (d) 82
  17. 17.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) 99 (b) 11 (c) 36 (d) 33
  18. 18.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 79 (c) 80 (d) 70
  19. 19.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 457 (d) 456
  20. 20.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 52 (c) 44 (d) 34
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 5 (b) 4 (c) 6 (d) 7
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15
  23. 23.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
  24. 24.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) 135 (b) 45 (c) 15 (d) 48
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  26. 26.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
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 13 (b) 15 (c) 5 (d) 14
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 6 (d) 17
  29. 29.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
  30. 30.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 494 (c) 634 (d) 633
  31. 31.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 160 (c) 178 (d) 169
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 13 (c) 14 (d) 3
  33. 33.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 291 (c) 266 (d) 282
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  35. 35.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 595 (d) 594
  36. 36.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 120 (c) 111 (d) 112
  37. 37.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 150 (d) 140
  38. 38.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 86 (c) 104 (d) 95
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 2 (d) 4
  40. 40.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) 54 (b) 17 (c) 51 (d) 153

Answer key

  1. 19
  2. 30
  3. 18
  4. 5
  5. 4
  6. 103
  7. 48
  8. 393
  9. 24
  10. 4
  11. 27
  12. 5
  13. 12
  14. 63
  15. 18
  16. 91
  17. 33
  18. 79
  19. 456
  20. 43
  21. 6
  22. 15
  23. 15
  24. 45
  25. 7
  26. 57
  27. 14
  28. 17
  29. 66
  30. 633
  31. 169
  32. 14
  33. 291
  34. 2
  35. 594
  36. 111
  37. 149
  38. 95
  39. 3
  40. 51

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