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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 610 · 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.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
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 18 (d) 17
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
  4. 4.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 549 (c) 558 (d) 444
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 20 (d) 21
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 4 (d) 3
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  9. 9.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) 69 (b) 198 (c) 22 (d) 66
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 18 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 20 (d) 8
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 2 (d) 5
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 3 (d) 4
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 5 (d) 4
  16. 16.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 152 (d) 160
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
  18. 18.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 360 (c) 351 (d) 361
  19. 19.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
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 6 (d) 17
  21. 21.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 271 (c) 270 (d) 252
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  23. 23.The numbers 20 to 28 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) 24 (c) 75 (d) 216
  24. 24.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) 45 (b) 15 (c) 18 (d) 5
  25. 25.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) 17 (b) 153 (c) 51 (d) 54
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 3 (b) 1 (c) 4 (d) 2
  27. 27.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 588 (b) 598 (c) 597 (d) 470
  28. 28.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 178 (c) 177 (d) 168
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 4 (c) 7 (d) 5
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 18 (c) 17 (d) 7
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 14 (c) 4 (d) 16
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  33. 33.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 264 (d) 274
  34. 34.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) 63 (b) 66 (c) 189 (d) 21
  35. 35.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
  36. 36.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) 99 (d) 33
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 18 (c) 16 (d) 17
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 1 (b) 3 (c) 4 (d) 2
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8

Answer key

  1. 54
  2. 18
  3. 17
  4. 558
  5. 2
  6. 20
  7. 5
  8. 19
  9. 66
  10. 19
  11. 3
  12. 19
  13. 4
  14. 4
  15. 4
  16. 151
  17. 9
  18. 360
  19. 18
  20. 16
  21. 270
  22. 2
  23. 72
  24. 15
  25. 51
  26. 3
  27. 597
  28. 177
  29. 6
  30. 17
  31. 15
  32. 4
  33. 273
  34. 63
  35. 65
  36. 33
  37. 17
  38. 16
  39. 3
  40. 8

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