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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 617 · 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.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) 21 (b) 63 (c) 189 (d) 66
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 17 (d) 16
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 11 (b) 10 (c) 9 (d) 4
  9. 9.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 643 (c) 500 (d) 633
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  11. 11.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 222 (c) 226 (d) 231
  12. 12.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) 60 (b) 20 (c) 180 (d) 63
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 8 (b) 6 (c) 7 (d) 9
  15. 15.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 165 (c) 166 (d) 174
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  19. 19.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 426 (c) 436 (d) 362
  20. 20.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 399 (c) 390 (d) 338
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 5 (c) 6 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 17 (b) 15 (c) 16 (d) 5
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 4 (d) 13
  27. 27.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 78 (d) 60
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  29. 29.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) 7 (b) 63 (c) 24 (d) 21
  30. 30.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 274 (d) 264
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 17 (d) 16
  32. 32.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) 6 (b) 54 (c) 21 (d) 18
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 17 (d) 19
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 7 (b) 9 (c) 8 (d) 10
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 18 (b) 9 (c) 19 (d) 20
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 5 (b) 7 (c) 8 (d) 6
  40. 40.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 170 (c) 152 (d) 162

Answer key

  1. 63
  2. 17
  3. 18
  4. 7
  5. 4
  6. 20
  7. 9
  8. 10
  9. 642
  10. 5
  11. 231
  12. 60
  13. 3
  14. 8
  15. 165
  16. 8
  17. 3
  18. 8
  19. 435
  20. 399
  21. 8
  22. 6
  23. 16
  24. 5
  25. 5
  26. 14
  27. 69
  28. 2
  29. 21
  30. 273
  31. 16
  32. 18
  33. 2
  34. 18
  35. 9
  36. 18
  37. 15
  38. 19
  39. 7
  40. 161

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