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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 780 · 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 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) 15 (c) 45 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  5. 5.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) 160 (c) 142 (d) 152
  6. 6.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 337 (c) 327 (d) 296
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 15 (b) 3 (c) 13 (d) 14
  9. 9.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) 18 (b) 57 (c) 54 (d) 162
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  12. 12.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 39 (d) 108
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 3 (b) 2 (c) 4 (d) 1
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 15 (d) 4
  16. 16.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 277 (c) 276 (d) 267
  17. 17.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
  18. 18.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 54 (d) 46
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 14 (d) 4
  20. 20.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) 72 (b) 27 (c) 24 (d) 8
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  22. 22.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 56 (c) 48 (d) 38
  23. 23.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 21 (d) 9
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 5 (b) 8 (c) 7 (d) 6
  27. 27.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 175 (c) 184 (d) 166
  28. 28.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) 60 (b) 171 (c) 19 (d) 57
  29. 29.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) 6 (d) 18
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 11 (c) 9 (d) 6
  31. 31.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
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  33. 33.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 116 (c) 98 (d) 107
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  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) 66 (b) 21 (c) 63 (d) 189
  36. 36.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 304 (c) 303 (d) 294
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 7 (c) 5 (d) 8
  38. 38.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) 75 (b) 72 (c) 216 (d) 24
  39. 39.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 348 (d) 349
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 4 (c) 2 (d) 5

Answer key

  1. 15
  2. 9
  3. 5
  4. 3
  5. 151
  6. 336
  7. 6
  8. 14
  9. 54
  10. 2
  11. 8
  12. 36
  13. 18
  14. 3
  15. 14
  16. 276
  17. 30
  18. 45
  19. 15
  20. 24
  21. 18
  22. 47
  23. 7
  24. 20
  25. 3
  26. 7
  27. 175
  28. 57
  29. 18
  30. 11
  31. 66
  32. 3
  33. 107
  34. 3
  35. 63
  36. 303
  37. 7
  38. 72
  39. 348
  40. 4

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