← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 160 · 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 two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  4. 4.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 39 (c) 108 (d) 12
  5. 5.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 142 (c) 151 (d) 160
  6. 6.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
  7. 7.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
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 10 (b) 12 (c) 11 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  11. 11.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) 6 (b) 54 (c) 18 (d) 21
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 18 (d) 19
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 13 (c) 7 (d) 12
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 7 (c) 6 (d) 5
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 14 (b) 4 (c) 13 (d) 15
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 19 (c) 17 (d) 18
  20. 20.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) 17 (c) 51 (d) 54
  21. 21.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) 19 (b) 171 (c) 57 (d) 60
  22. 22.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 393 (c) 402 (d) 403
  23. 23.The numbers 10 to 18 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) 45 (c) 14 (d) 126
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 3 (b) 5 (c) 6 (d) 4
  25. 25.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) 37 (d) 28
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 6 (b) 16 (c) 17 (d) 18
  27. 27.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) 72 (b) 8 (c) 24 (d) 27
  28. 28.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 158 (c) 176 (d) 167
  29. 29.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 228 (c) 238 (d) 230
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  31. 31.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 183 (d) 192
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 4 (c) 6 (d) 5
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 5 (b) 3 (c) 4 (d) 6
  34. 34.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 579 (c) 458 (d) 570
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  36. 36.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 356 (d) 426
  37. 37.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 310 (c) 309 (d) 278
  38. 38.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
  39. 39.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 196 (c) 187 (d) 188
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3

Answer key

  1. 3
  2. 8
  3. 8
  4. 36
  5. 151
  6. 21
  7. 69
  8. 11
  9. 5
  10. 3
  11. 18
  12. 4
  13. 20
  14. 19
  15. 12
  16. 2
  17. 6
  18. 14
  19. 18
  20. 51
  21. 57
  22. 402
  23. 42
  24. 5
  25. 37
  26. 17
  27. 24
  28. 167
  29. 237
  30. 5
  31. 192
  32. 5
  33. 5
  34. 579
  35. 4
  36. 426
  37. 309
  38. 54
  39. 187
  40. 2

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