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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 666 · 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 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 20 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  3. 3.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) 64 (c) 63 (d) 72
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 5 (d) 4
  6. 6.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) 9 (b) 27 (c) 30 (d) 81
  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) 16 (c) 51 (d) 48
  8. 8.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) 33 (b) 99 (c) 11 (d) 36
  9. 9.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 402 (c) 412 (d) 411
  10. 10.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 470 (c) 597 (d) 598
  11. 11.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 132 (c) 150 (d) 141
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  13. 13.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 108 (c) 126 (d) 117
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  16. 16.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 438 (c) 439 (d) 429
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 3 (d) 4
  18. 18.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) 63 (d) 180
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 3 (d) 5
  20. 20.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 183 (c) 192 (d) 193
  21. 21.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) 42 (c) 13 (d) 117
  22. 22.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 234 (c) 243 (d) 244
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 6 (d) 17
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 16 (d) 17
  26. 26.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 219 (c) 229 (d) 228
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 21 (d) 19
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 19 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 18 (d) 7
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 7 (b) 9 (c) 10 (d) 8
  32. 32.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) 45 (c) 135 (d) 48
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  34. 34.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) 72 (b) 24 (c) 8 (d) 27
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 6 (b) 4 (c) 3 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
  38. 38.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) 18 (d) 6
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
  40. 40.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 270 (c) 297 (d) 298

Answer key

  1. 19
  2. 3
  3. 63
  4. 5
  5. 5
  6. 27
  7. 48
  8. 33
  9. 411
  10. 597
  11. 141
  12. 4
  13. 117
  14. 7
  15. 19
  16. 438
  17. 3
  18. 60
  19. 4
  20. 192
  21. 39
  22. 243
  23. 20
  24. 16
  25. 17
  26. 228
  27. 20
  28. 18
  29. 9
  30. 18
  31. 9
  32. 45
  33. 8
  34. 24
  35. 5
  36. 8
  37. 14
  38. 18
  39. 18
  40. 297

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