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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 116 · 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 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 354 (c) 364 (d) 363
  2. 2.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 51 (c) 17 (d) 54
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 17 (d) 7
  4. 4.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 140 (c) 132 (d) 131
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 7 (c) 4 (d) 8
  6. 6.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 220 (c) 210 (d) 219
  7. 7.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 18 (d) 57
  8. 8.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 301 (c) 272 (d) 300
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 3 (d) 1
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 7 (b) 6 (c) 5 (d) 8
  12. 12.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 577 (c) 456 (d) 567
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 7 (b) 6 (c) 5 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 5 (b) 6 (c) 3 (d) 4
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 19 (d) 18
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  19. 19.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) 66 (b) 198 (c) 69 (d) 22
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 10 (c) 3 (d) 9
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 3 (d) 5
  23. 23.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 255 (c) 256 (d) 246
  24. 24.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 480 (d) 471
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 17 (c) 5 (d) 15
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 6 (b) 12 (c) 10 (d) 13
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 9 (b) 12 (c) 6 (d) 11
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 4 (d) 15
  30. 30.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 39 (c) 30 (d) 40
  31. 31.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 366 (c) 367 (d) 357
  32. 32.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  33. 33.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 136 (c) 135 (d) 144
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 17
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 17 (c) 7 (d) 18
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 15 (c) 13 (d) 14
  37. 37.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) 21 (b) 63 (c) 7 (d) 24
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 2 (d) 4
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 15 (b) 14 (c) 16 (d) 4
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 2 (d) 5

Answer key

  1. 363
  2. 51
  3. 18
  4. 131
  5. 7
  6. 219
  7. 54
  8. 300
  9. 9
  10. 3
  11. 7
  12. 576
  13. 7
  14. 9
  15. 3
  16. 5
  17. 18
  18. 5
  19. 66
  20. 4
  21. 9
  22. 4
  23. 255
  24. 480
  25. 8
  26. 16
  27. 12
  28. 11
  29. 15
  30. 39
  31. 366
  32. 4
  33. 135
  34. 16
  35. 17
  36. 14
  37. 21
  38. 4
  39. 15
  40. 4

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