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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 74 · 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 two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 2 (d) 4
  3. 3.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) 108 (b) 39 (c) 12 (d) 36
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 17 (b) 16 (c) 5 (d) 15
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 16 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  7. 7.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
  8. 8.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 56 (c) 64 (d) 46
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 16 (d) 14
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 21 (d) 20
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 9 (b) 7 (c) 8 (d) 6
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  16. 16.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 480 (c) 398 (d) 489
  17. 17.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) 18 (b) 54 (c) 57 (d) 162
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
  21. 21.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) 69 (c) 22 (d) 198
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 18 (d) 17
  23. 23.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) 9 (c) 30 (d) 27
  24. 24.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 493 (b) 400 (c) 492 (d) 483
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 20 (d) 21
  26. 26.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 208 (c) 198 (d) 210
  27. 27.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 83 (c) 92 (d) 84
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 7 (b) 9 (c) 8 (d) 6
  29. 29.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 140 (c) 131 (d) 122
  30. 30.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
  31. 31.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 216 (c) 226 (d) 225
  32. 32.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 288 (c) 279 (d) 264
  33. 33.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 378 (c) 459 (d) 460
  34. 34.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 156 (c) 147 (d) 148
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 14 (d) 13
  37. 37.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 238 (c) 230 (d) 237
  38. 38.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) 10 (c) 33 (d) 30
  39. 39.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 164 (c) 174 (d) 182
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16

Answer key

  1. 6
  2. 4
  3. 36
  4. 16
  5. 16
  6. 2
  7. 567
  8. 55
  9. 15
  10. 20
  11. 5
  12. 3
  13. 8
  14. 4
  15. 2
  16. 489
  17. 54
  18. 9
  19. 9
  20. 18
  21. 66
  22. 17
  23. 27
  24. 492
  25. 20
  26. 207
  27. 83
  28. 8
  29. 131
  30. 60
  31. 225
  32. 288
  33. 459
  34. 147
  35. 4
  36. 14
  37. 237
  38. 30
  39. 173
  40. 4

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