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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 671 · 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 15? (a) 4 (b) 3 (c) 16 (d) 5
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 18 (d) 6
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 16 (d) 17
  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) 48 (b) 45 (c) 15 (d) 135
  5. 5.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 46 (c) 36 (d) 54
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 16 (d) 17
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 6 (b) 7 (c) 5 (d) 4
  10. 10.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) 63 (b) 60 (c) 20 (d) 180
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  13. 13.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 186 (c) 196 (d) 195
  14. 14.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 588 (c) 598 (d) 597
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 8 (c) 7 (d) 5
  16. 16.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) 57 (b) 60 (c) 19 (d) 171
  17. 17.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 94 (d) 85
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 1 (d) 3
  20. 20.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) 144 (b) 51 (c) 16 (d) 48
  21. 21.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 50 (c) 59 (d) 68
  22. 22.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 440 (b) 552 (c) 543 (d) 553
  23. 23.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) 21 (b) 54 (c) 18 (d) 6
  24. 24.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) 72 (b) 207 (c) 69 (d) 23
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 18 (d) 6
  27. 27.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 75 (c) 76 (d) 84
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 18 (d) 7
  29. 29.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 294 (c) 324 (d) 334
  30. 30.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 375 (b) 366 (c) 322 (d) 376
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 5 (c) 6 (d) 3
  32. 32.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 158 (c) 176 (d) 168
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 14 (b) 13 (c) 3 (d) 15
  34. 34.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 427 (c) 417 (d) 356
  35. 35.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
  36. 36.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 628 (c) 627 (d) 618
  37. 37.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 40 (c) 31 (d) 22
  38. 38.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 52 (c) 61 (d) 62
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7

Answer key

  1. 4
  2. 17
  3. 16
  4. 45
  5. 45
  6. 4
  7. 3
  8. 17
  9. 6
  10. 60
  11. 9
  12. 9
  13. 195
  14. 597
  15. 7
  16. 57
  17. 85
  18. 5
  19. 3
  20. 48
  21. 59
  22. 552
  23. 18
  24. 69
  25. 3
  26. 17
  27. 75
  28. 18
  29. 333
  30. 375
  31. 5
  32. 167
  33. 14
  34. 426
  35. 63
  36. 627
  37. 31
  38. 61
  39. 4
  40. 8

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