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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 885 · 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 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) 57 (b) 19 (c) 60 (d) 171
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 18 (b) 6 (c) 16 (d) 17
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 3 (d) 2
  5. 5.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 405 (c) 415 (d) 348
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  7. 7.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) 10 (c) 90 (d) 33
  8. 8.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 38 (d) 47
  9. 9.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) 75 (b) 24 (c) 72 (d) 216
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  12. 12.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) 24 (c) 72 (d) 27
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 9 (b) 12 (c) 11 (d) 6
  14. 14.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) 72 (c) 207 (d) 69
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 5 (c) 6 (d) 3
  16. 16.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 357 (d) 358
  17. 17.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 324 (d) 288
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
  19. 19.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) 15 (c) 45 (d) 48
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  21. 21.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 166 (c) 156 (d) 165
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  24. 24.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 142 (c) 151 (d) 152
  25. 25.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 21 (b) 9 (c) 20 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 9 (b) 20 (c) 19 (d) 21
  30. 30.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 211 (c) 201 (d) 212
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 18
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 14 (d) 15
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  35. 35.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 318 (c) 328 (d) 327
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 14 (b) 5 (c) 13 (d) 12
  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) 158 (b) 140 (c) 150 (d) 149
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 16 (d) 17
  39. 39.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) 54 (d) 162
  40. 40.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 88 (c) 80 (d) 79

Answer key

  1. 57
  2. 9
  3. 17
  4. 4
  5. 414
  6. 7
  7. 30
  8. 47
  9. 72
  10. 6
  11. 2
  12. 24
  13. 11
  14. 69
  15. 5
  16. 357
  17. 324
  18. 19
  19. 45
  20. 4
  21. 165
  22. 4
  23. 5
  24. 151
  25. 8
  26. 18
  27. 20
  28. 3
  29. 20
  30. 210
  31. 20
  32. 19
  33. 14
  34. 6
  35. 327
  36. 13
  37. 149
  38. 16
  39. 54
  40. 79

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