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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 86 · 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.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 187 (c) 196 (d) 178
  2. 2.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 328 (c) 290 (d) 327
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 20 (d) 18
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  5. 5.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) 108 (d) 36
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 8 (d) 20
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 18 (d) 20
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  11. 11.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 160 (d) 159
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  13. 13.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) 42 (b) 39 (c) 13 (d) 117
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 5 (d) 6
  15. 15.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 433 (c) 423 (d) 432
  16. 16.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) 189 (b) 21 (c) 63 (d) 66
  17. 17.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) 216 (c) 24 (d) 75
  18. 18.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 349 (c) 339 (d) 348
  19. 19.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
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 7 (c) 5 (d) 8
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 5 (b) 6 (c) 8 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  23. 23.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 89 (c) 80 (d) 90
  24. 24.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) 11 (c) 99 (d) 33
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  26. 26.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 127 (c) 128 (d) 136
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  28. 28.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 212 (c) 210 (d) 211
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 3 (d) 4
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  32. 32.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 258 (d) 259
  33. 33.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 416 (c) 507 (d) 517
  34. 34.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) 69 (b) 22 (c) 66 (d) 198
  35. 35.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 96 (c) 95 (d) 104
  36. 36.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  37. 37.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 181 (c) 182 (d) 172
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 4 (d) 6
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 6 (c) 3 (d) 5
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 5 (d) 4

Answer key

  1. 187
  2. 327
  3. 19
  4. 5
  5. 36
  6. 19
  7. 5
  8. 8
  9. 19
  10. 8
  11. 159
  12. 7
  13. 39
  14. 5
  15. 432
  16. 63
  17. 72
  18. 348
  19. 27
  20. 7
  21. 7
  22. 2
  23. 89
  24. 33
  25. 5
  26. 127
  27. 19
  28. 210
  29. 3
  30. 3
  31. 2
  32. 258
  33. 516
  34. 66
  35. 95
  36. 600
  37. 181
  38. 5
  39. 5
  40. 6

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