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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 208 · 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 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 20
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  6. 6.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 325 (d) 324
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  8. 8.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 28 (d) 46
  9. 9.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 173 (d) 182
  10. 10.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 462 (c) 453 (d) 380
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 5 (d) 3
  12. 12.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) 168 (d) 167
  13. 13.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 541 (d) 540
  14. 14.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) 615 (d) 482
  15. 15.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) 198 (b) 69 (c) 22 (d) 66
  16. 16.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 338 (d) 399
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 16 (b) 17 (c) 5 (d) 15
  18. 18.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 15 (c) 135 (d) 45
  19. 19.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 50 (d) 49
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 17 (d) 8
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 17 (c) 8 (d) 18
  22. 22.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 628 (c) 627 (d) 490
  23. 23.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 42 (d) 41
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  25. 25.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 111 (d) 112
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 5 (c) 6 (d) 7
  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) 27 (b) 8 (c) 72 (d) 24
  28. 28.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 210 (c) 211 (d) 212
  29. 29.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 343 (d) 300
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  32. 32.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) 10 (b) 33 (c) 90 (d) 30
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19
  34. 34.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 254 (c) 273 (d) 264
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 5 (d) 16
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  38. 38.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) 17 (d) 54
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 19 (d) 18
  40. 40.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 639 (c) 630 (d) 498

Answer key

  1. 19
  2. 2
  3. 5
  4. 5
  5. 8
  6. 324
  7. 4
  8. 37
  9. 173
  10. 462
  11. 5
  12. 167
  13. 540
  14. 615
  15. 66
  16. 399
  17. 16
  18. 45
  19. 49
  20. 18
  21. 18
  22. 627
  23. 41
  24. 7
  25. 111
  26. 6
  27. 24
  28. 210
  29. 342
  30. 4
  31. 19
  32. 30
  33. 19
  34. 273
  35. 16
  36. 6
  37. 5
  38. 51
  39. 19
  40. 639

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