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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 246 · 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 15? (a) 3 (b) 4 (c) 5 (d) 16
  2. 2.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 387 (d) 336
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 14 (d) 16
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 13 (d) 14
  5. 5.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 502 (c) 501 (d) 492
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  7. 7.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 98 (c) 116 (d) 108
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  9. 9.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 372 (c) 373 (d) 320
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 5 (c) 6 (d) 4
  12. 12.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) 57 (c) 171 (d) 60
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 6 (d) 16
  14. 14.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 574 (c) 564 (d) 573
  15. 15.The numbers 3 to 11 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) 63 (c) 7 (d) 21
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  18. 18.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) 216 (c) 72 (d) 24
  19. 19.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 175 (c) 184 (d) 176
  20. 20.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 308 (c) 345 (d) 355
  21. 21.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 333 (c) 334 (d) 294
  22. 22.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
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 15 (b) 16 (c) 4 (d) 14
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  26. 26.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 160 (c) 159 (d) 168
  27. 27.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 157 (c) 148 (d) 166
  28. 28.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) 45 (b) 18 (c) 5 (d) 15
  29. 29.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) 10 (b) 30 (c) 33 (d) 90
  30. 30.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 576 (c) 456 (d) 577
  31. 31.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
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 8 (d) 7
  34. 34.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 164 (c) 172 (d) 154
  35. 35.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 112 (c) 102 (d) 120
  36. 36.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) 48 (c) 51 (d) 16
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  38. 38.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  39. 39.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
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 4 (d) 5

Answer key

  1. 4
  2. 396
  3. 15
  4. 14
  5. 501
  6. 4
  7. 107
  8. 7
  9. 372
  10. 9
  11. 6
  12. 57
  13. 17
  14. 573
  15. 21
  16. 2
  17. 7
  18. 72
  19. 175
  20. 354
  21. 333
  22. 19
  23. 6
  24. 15
  25. 2
  26. 159
  27. 157
  28. 15
  29. 30
  30. 576
  31. 36
  32. 8
  33. 7
  34. 163
  35. 111
  36. 48
  37. 8
  38. 3
  39. 8
  40. 4

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