← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 862 · 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 6 written when you write all the numbers from 1 to 52? (a) 5 (b) 3 (c) 4 (d) 6
  2. 2.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
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 17 (d) 16
  5. 5.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 429 (c) 358 (d) 430
  6. 6.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) 338 (c) 399 (d) 390
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 5 (d) 4
  9. 9.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) 33 (c) 11 (d) 36
  10. 10.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 74 (d) 84
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 7 (c) 5 (d) 8
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 9 (b) 6 (c) 4 (d) 8
  13. 13.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 280 (c) 303 (d) 313
  14. 14.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 108 (c) 118 (d) 126
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 6 (d) 4
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  17. 17.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 189 (c) 198 (d) 180
  18. 18.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 516 (d) 525
  19. 19.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) 27 (b) 30 (c) 9 (d) 81
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 14 (b) 15 (c) 13 (d) 3
  21. 21.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 106 (c) 124 (d) 115
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 4 (d) 2
  23. 23.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) 18 (c) 57 (d) 162
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 20 (d) 21
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  27. 27.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 272 (c) 291 (d) 300
  28. 28.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) 22 (b) 66 (c) 69 (d) 198
  29. 29.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 123 (d) 124
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 3 (d) 2
  31. 31.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 69 (c) 207 (d) 72
  32. 32.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 176 (c) 167 (d) 168
  33. 33.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 127 (c) 118 (d) 128
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  35. 35.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 327 (c) 296 (d) 337
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 3 (d) 13
  38. 38.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 195 (c) 196 (d) 186
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  40. 40.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) 144 (b) 16 (c) 51 (d) 48

Answer key

  1. 5
  2. 21
  3. 3
  4. 16
  5. 429
  6. 399
  7. 20
  8. 5
  9. 33
  10. 83
  11. 7
  12. 8
  13. 312
  14. 117
  15. 5
  16. 20
  17. 189
  18. 525
  19. 27
  20. 14
  21. 115
  22. 4
  23. 54
  24. 2
  25. 20
  26. 16
  27. 300
  28. 66
  29. 123
  30. 3
  31. 69
  32. 167
  33. 127
  34. 6
  35. 336
  36. 8
  37. 14
  38. 195
  39. 4
  40. 48

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad