← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 88 · 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.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) 16 (b) 51 (c) 144 (d) 48
  2. 2.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 378 (d) 324
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  4. 4.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) 18 (b) 57 (c) 54 (d) 162
  5. 5.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) 42 (b) 39 (c) 117 (d) 13
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 17
  7. 7.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 180 (c) 190 (d) 198
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  9. 9.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 90 (d) 81
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 14 (d) 3
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
  13. 13.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 130 (c) 140 (d) 139
  14. 14.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 361 (c) 351 (d) 312
  15. 15.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 187 (c) 188 (d) 178
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 2 (d) 4
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 21
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 4 (d) 6
  20. 20.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
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 9 (b) 14 (c) 13 (d) 11
  22. 22.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 243 (c) 253 (d) 240
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 3 (d) 4
  24. 24.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) 17 (b) 51 (c) 54 (d) 153
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  28. 28.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) 11 (c) 99 (d) 36
  29. 29.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 316 (c) 282 (d) 306
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  32. 32.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 45 (c) 5 (d) 15
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 9 (c) 10 (d) 8
  34. 34.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) 63 (d) 189
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 4 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  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) 24 (b) 21 (c) 63 (d) 7
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  39. 39.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) 18 (b) 6 (c) 21 (d) 54
  40. 40.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 46 (c) 56 (d) 64

Answer key

  1. 48
  2. 378
  3. 4
  4. 54
  5. 39
  6. 18
  7. 189
  8. 8
  9. 81
  10. 5
  11. 14
  12. 5
  13. 139
  14. 360
  15. 187
  16. 4
  17. 3
  18. 20
  19. 5
  20. 60
  21. 13
  22. 252
  23. 4
  24. 51
  25. 2
  26. 9
  27. 9
  28. 33
  29. 315
  30. 7
  31. 19
  32. 15
  33. 9
  34. 63
  35. 3
  36. 4
  37. 21
  38. 6
  39. 18
  40. 55

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