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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 485 · 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 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 225 (d) 234
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 19 (d) 18
  3. 3.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) 18 (c) 57 (d) 162
  4. 4.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) 135 (b) 15 (c) 45 (d) 48
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 19 (d) 18
  6. 6.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) 11 (b) 36 (c) 33 (d) 99
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  8. 8.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) 51 (b) 48 (c) 144 (d) 16
  9. 9.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) 458 (c) 579 (d) 570
  10. 10.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) 8 (b) 27 (c) 24 (d) 72
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 15 (c) 13 (d) 14
  12. 12.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) 21 (b) 63 (c) 189 (d) 66
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 9 (d) 19
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  16. 16.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 555 (c) 546 (d) 442
  17. 17.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 352 (c) 411 (d) 421
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 19 (b) 17 (c) 8 (d) 18
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  21. 21.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) 32 (d) 40
  22. 22.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 342 (c) 396 (d) 406
  23. 23.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 108 (c) 100 (d) 99
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 2 (d) 3
  26. 26.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) 351 (c) 312 (d) 361
  27. 27.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 436 (c) 435 (d) 426
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 5 (d) 3
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 14 (b) 7 (c) 13 (d) 11
  30. 30.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 156 (c) 166 (d) 174
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 9 (b) 18 (c) 19 (d) 16
  33. 33.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 128 (c) 138 (d) 137
  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) 30 (d) 10
  35. 35.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 201 (d) 211
  36. 36.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  37. 37.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) 72 (c) 69 (d) 23
  38. 38.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 351 (c) 342 (d) 352
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 15 (d) 5
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 15 (d) 16

Answer key

  1. 234
  2. 18
  3. 54
  4. 45
  5. 18
  6. 33
  7. 3
  8. 48
  9. 579
  10. 24
  11. 14
  12. 63
  13. 19
  14. 9
  15. 2
  16. 555
  17. 420
  18. 18
  19. 3
  20. 6
  21. 31
  22. 405
  23. 99
  24. 3
  25. 4
  26. 360
  27. 435
  28. 5
  29. 13
  30. 165
  31. 3
  32. 18
  33. 137
  34. 30
  35. 210
  36. 4
  37. 69
  38. 351
  39. 15
  40. 15

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