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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 157 · 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 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) 21 (c) 54 (d) 18
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 17
  3. 3.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 386 (c) 462 (d) 472
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 18 (d) 16
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  8. 8.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) 9 (b) 81 (c) 30 (d) 27
  9. 9.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 369 (c) 318 (d) 370
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 7 (d) 18
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 12 (c) 13 (d) 3
  12. 12.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) 66 (c) 69 (d) 22
  13. 13.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 166 (d) 165
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  15. 15.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 288 (d) 279
  16. 16.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 66 (c) 76 (d) 84
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  18. 18.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) 189 (c) 66 (d) 63
  19. 19.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) 72 (d) 24
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 7 (b) 4 (c) 5 (d) 6
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 7 (b) 8 (c) 5 (d) 6
  22. 22.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 156 (c) 138 (d) 147
  23. 23.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 55 (c) 56 (d) 64
  24. 24.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 158 (c) 148 (d) 157
  25. 25.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 13 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  28. 28.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 309 (d) 310
  29. 29.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 45 (c) 14 (d) 42
  30. 30.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) 5 (c) 45 (d) 15
  31. 31.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) 90 (b) 33 (c) 30 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 3 (d) 2
  34. 34.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) 117 (b) 42 (c) 13 (d) 39
  35. 35.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 307 (c) 297 (d) 306
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 9 (b) 12 (c) 11 (d) 7
  40. 40.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 284 (c) 318 (d) 309

Answer key

  1. 18
  2. 18
  3. 471
  4. 5
  5. 17
  6. 8
  7. 6
  8. 27
  9. 369
  10. 17
  11. 12
  12. 66
  13. 165
  14. 18
  15. 288
  16. 75
  17. 2
  18. 63
  19. 24
  20. 6
  21. 7
  22. 147
  23. 55
  24. 157
  25. 6
  26. 14
  27. 8
  28. 309
  29. 42
  30. 15
  31. 30
  32. 2
  33. 3
  34. 39
  35. 306
  36. 5
  37. 18
  38. 18
  39. 11
  40. 318

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