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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 783 · 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 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 92 (c) 82 (d) 91
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 17 (b) 8 (c) 19 (d) 18
  3. 3.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) 198 (d) 66
  4. 4.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  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) 30 (b) 9 (c) 27 (d) 81
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 8 (d) 18
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 8 (c) 3 (d) 9
  9. 9.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 240 (c) 250 (d) 249
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  12. 12.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 193 (c) 192 (d) 200
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  14. 14.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 82 (c) 64 (d) 73
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 19 (d) 18
  16. 16.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) 12 (b) 39 (c) 36 (d) 108
  17. 17.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) 171 (b) 60 (c) 57 (d) 19
  18. 18.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 460 (d) 459
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 19 (b) 8 (c) 20 (d) 18
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 15 (d) 16
  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) 117 (b) 42 (c) 13 (d) 39
  22. 22.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 537 (d) 538
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 7 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  26. 26.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 589 (c) 588 (d) 464
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  28. 28.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 600 (c) 609 (d) 478
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 5 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 4 (d) 5
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  33. 33.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 220 (c) 222 (d) 213
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 7 (c) 10 (d) 13
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 7 (d) 19
  36. 36.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 178 (c) 187 (d) 188
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 13 (d) 14
  38. 38.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) 99 (b) 11 (c) 36 (d) 33
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  40. 40.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 355 (c) 308 (d) 354

Answer key

  1. 91
  2. 18
  3. 66
  4. 5
  5. 19
  6. 27
  7. 18
  8. 9
  9. 249
  10. 18
  11. 2
  12. 192
  13. 16
  14. 73
  15. 18
  16. 36
  17. 57
  18. 459
  19. 19
  20. 15
  21. 39
  22. 537
  23. 6
  24. 3
  25. 2
  26. 588
  27. 6
  28. 609
  29. 4
  30. 4
  31. 4
  32. 18
  33. 222
  34. 12
  35. 18
  36. 187
  37. 14
  38. 33
  39. 3
  40. 354

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