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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 537 · 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 times is the digit 4 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 17 (d) 16
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 3 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 18 (b) 19 (c) 17 (d) 7
  6. 6.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) 8 (b) 24 (c) 27 (d) 72
  7. 7.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 90 (c) 108 (d) 99
  8. 8.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) 54 (b) 51 (c) 17 (d) 153
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  10. 10.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) 24 (d) 72
  11. 11.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 574 (c) 564 (d) 454
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 4 (d) 14
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 14 (d) 15
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  16. 16.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 114 (d) 132
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  19. 19.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 38 (c) 28 (d) 37
  20. 20.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) 57 (b) 19 (c) 60 (d) 171
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
  23. 23.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 152 (d) 160
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 6 (d) 16
  26. 26.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 166 (c) 175 (d) 184
  27. 27.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 248 (c) 255 (d) 264
  28. 28.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
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 15 (b) 3 (c) 14 (d) 13
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 3 (d) 1
  32. 32.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 252 (d) 261
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 5 (c) 3 (d) 4
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 17 (b) 18 (c) 16 (d) 6
  36. 36.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) 33 (c) 30 (d) 90
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 17 (b) 5 (c) 16 (d) 15
  39. 39.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 321 (d) 322
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 6 (b) 5 (c) 3 (d) 4

Answer key

  1. 16
  2. 9
  3. 4
  4. 8
  5. 18
  6. 24
  7. 99
  8. 51
  9. 4
  10. 72
  11. 573
  12. 18
  13. 14
  14. 15
  15. 5
  16. 123
  17. 6
  18. 9
  19. 37
  20. 57
  21. 7
  22. 4
  23. 151
  24. 3
  25. 16
  26. 175
  27. 264
  28. 339
  29. 14
  30. 20
  31. 3
  32. 270
  33. 5
  34. 4
  35. 17
  36. 30
  37. 6
  38. 16
  39. 321
  40. 5

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