← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 495 · 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 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 540 (c) 549 (d) 438
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 8 (d) 17
  4. 4.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 510 (c) 418 (d) 519
  5. 5.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
  6. 6.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) 132 (d) 114
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 17 (d) 16
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 4 (d) 3
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 4 (d) 3
  11. 11.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 628 (c) 618 (d) 490
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  13. 13.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 273 (c) 274 (d) 254
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 19 (d) 21
  15. 15.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) 13 (b) 117 (c) 39 (d) 42
  16. 16.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) 15 (c) 45 (d) 5
  17. 17.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 328 (c) 318 (d) 327
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  19. 19.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
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  21. 21.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) 108 (b) 12 (c) 36 (d) 39
  22. 22.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) 24 (c) 21 (d) 63
  23. 23.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 219 (c) 228 (d) 224
  24. 24.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) 66 (b) 69 (c) 22 (d) 198
  25. 25.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 462 (c) 386 (d) 471
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 15 (d) 16
  28. 28.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 265 (c) 255 (d) 264
  29. 29.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 204 (c) 208 (d) 195
  30. 30.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 74 (c) 66 (d) 65
  31. 31.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) 189 (b) 63 (c) 66 (d) 21
  32. 32.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) 207 (b) 23 (c) 69 (d) 72
  33. 33.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) 162 (c) 57 (d) 54
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  35. 35.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 321 (c) 312 (d) 286
  36. 36.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) 126 (c) 108 (d) 118
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  38. 38.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 252 (c) 243 (d) 253
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 16 (d) 17
  40. 40.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 143 (c) 144 (d) 134

Answer key

  1. 549
  2. 7
  3. 18
  4. 519
  5. 27
  6. 123
  7. 5
  8. 16
  9. 4
  10. 5
  11. 627
  12. 7
  13. 273
  14. 20
  15. 39
  16. 15
  17. 327
  18. 3
  19. 14
  20. 5
  21. 36
  22. 21
  23. 228
  24. 66
  25. 471
  26. 4
  27. 15
  28. 264
  29. 204
  30. 65
  31. 63
  32. 69
  33. 54
  34. 9
  35. 321
  36. 117
  37. 9
  38. 252
  39. 16
  40. 143

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