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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 807 · 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 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) 27 (b) 72 (c) 8 (d) 24
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 15 (c) 16 (d) 8
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 5 (b) 4 (c) 2 (d) 3
  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) 160 (b) 152 (c) 142 (d) 151
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  7. 7.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 186 (c) 185 (d) 176
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  9. 9.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 610 (c) 478 (d) 600
  10. 10.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
  11. 11.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 32 (c) 40 (d) 31
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 15 (d) 13
  14. 14.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) 153 (b) 17 (c) 51 (d) 54
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 6 (d) 16
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  18. 18.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 112 (c) 130 (d) 121
  19. 19.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) 45 (b) 135 (c) 15 (d) 48
  20. 20.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) 10 (d) 30
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  24. 24.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327
  25. 25.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) 66 (c) 63 (d) 189
  26. 26.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 492 (c) 501 (d) 406
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 17 (d) 6
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 3 (c) 1 (d) 2
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  30. 30.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) 12 (b) 108 (c) 39 (d) 36
  31. 31.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 228 (c) 229 (d) 219
  32. 32.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 504 (c) 495 (d) 408
  33. 33.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 124 (c) 106 (d) 116
  34. 34.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) 33 (b) 11 (c) 36 (d) 99
  35. 35.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) 15 (b) 18 (c) 45 (d) 5
  36. 36.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) 22 (d) 69
  37. 37.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 286 (d) 322
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 13 (c) 9 (d) 15
  40. 40.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10

Answer key

  1. 24
  2. 4
  3. 15
  4. 4
  5. 151
  6. 2
  7. 185
  8. 5
  9. 609
  10. 48
  11. 31
  12. 8
  13. 14
  14. 51
  15. 17
  16. 309
  17. 3
  18. 121
  19. 45
  20. 30
  21. 4
  22. 4
  23. 4
  24. 336
  25. 63
  26. 501
  27. 17
  28. 3
  29. 20
  30. 36
  31. 228
  32. 504
  33. 115
  34. 33
  35. 15
  36. 66
  37. 321
  38. 17
  39. 15
  40. 6

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