← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 267 · 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 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 133 (d) 134
  2. 2.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) 24 (b) 8 (c) 72 (d) 27
  3. 3.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 294 (c) 268 (d) 295
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 4 (b) 5 (c) 3 (d) 6
  5. 5.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) 180 (b) 20 (c) 63 (d) 60
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 21
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  8. 8.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 39 (d) 13
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 4 (d) 15
  10. 10.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) 72 (b) 69 (c) 23 (d) 207
  11. 11.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 285 (c) 262 (d) 286
  12. 12.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 454 (c) 564 (d) 573
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  14. 14.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) 66 (b) 21 (c) 189 (d) 63
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 6 (d) 4
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  17. 17.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 363 (c) 320 (d) 372
  18. 18.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) 33 (b) 36 (c) 11 (d) 99
  19. 19.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 247 (c) 246 (d) 237
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  21. 21.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 482 (d) 615
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  23. 23.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 134 (c) 143 (d) 152
  24. 24.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 160 (c) 168 (d) 159
  25. 25.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) 171 (b) 60 (c) 57 (d) 19
  26. 26.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 532 (c) 426 (d) 531
  27. 27.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) 51 (b) 153 (c) 54 (d) 17
  28. 28.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 106 (c) 96 (d) 114
  29. 29.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 22 (c) 40 (d) 32
  30. 30.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) 72 (b) 216 (c) 75 (d) 24
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 7 (d) 16
  34. 34.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) 33 (b) 90 (c) 10 (d) 30
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 4 (d) 1
  36. 36.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 172 (c) 162 (d) 180
  37. 37.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 62 (d) 53
  38. 38.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 62 (d) 61
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 13 (d) 12
  40. 40.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 421 (c) 352 (d) 420

Answer key

  1. 133
  2. 24
  3. 294
  4. 5
  5. 60
  6. 20
  7. 9
  8. 39
  9. 15
  10. 69
  11. 285
  12. 573
  13. 3
  14. 63
  15. 5
  16. 4
  17. 372
  18. 33
  19. 246
  20. 8
  21. 615
  22. 8
  23. 143
  24. 159
  25. 57
  26. 531
  27. 51
  28. 105
  29. 31
  30. 72
  31. 17
  32. 9
  33. 17
  34. 30
  35. 3
  36. 171
  37. 53
  38. 61
  39. 13
  40. 420

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