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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 994 · 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 4? (a) 10 (b) 4 (c) 5 (d) 3
  2. 2.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 204 (c) 198 (d) 189
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 1
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 4 (d) 5
  7. 7.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 340 (c) 298 (d) 339
  8. 8.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 612 (c) 622 (d) 621
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 8 (c) 5 (d) 7
  10. 10.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) 63 (b) 20 (c) 180 (d) 60
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 16 (b) 18 (c) 6 (d) 17
  12. 12.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 96 (d) 105
  13. 13.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 370 (c) 360 (d) 369
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 19 (d) 7
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 15 (c) 14 (d) 3
  17. 17.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 465 (c) 475 (d) 474
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 15 (c) 16 (d) 5
  20. 20.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 32 (c) 40 (d) 31
  21. 21.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) 21 (b) 54 (c) 6 (d) 18
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 9 (d) 19
  23. 23.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) 24 (c) 72 (d) 216
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 18 (d) 9
  25. 25.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 24 (d) 8
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 18 (d) 9
  27. 27.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 4 (d) 3
  29. 29.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 567 (c) 576 (d) 456
  30. 30.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
  31. 31.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 202 (c) 196 (d) 186
  32. 32.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) 51 (b) 48 (c) 16 (d) 144
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  35. 35.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 66 (d) 76
  36. 36.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 612 (c) 480 (d) 613
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 18 (d) 19
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

  1. 4
  2. 198
  3. 2
  4. 6
  5. 3
  6. 6
  7. 339
  8. 621
  9. 7
  10. 60
  11. 17
  12. 105
  13. 369
  14. 18
  15. 3
  16. 14
  17. 474
  18. 19
  19. 15
  20. 31
  21. 18
  22. 19
  23. 72
  24. 19
  25. 24
  26. 19
  27. 81
  28. 4
  29. 576
  30. 36
  31. 195
  32. 48
  33. 5
  34. 8
  35. 75
  36. 612
  37. 7
  38. 18
  39. 9
  40. 3

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