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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 358 · 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 16? (a) 2 (b) 3 (c) 4 (d) 17
  2. 2.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) 8 (c) 27 (d) 24
  3. 3.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 516 (c) 517 (d) 416
  4. 4.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) 30 (b) 10 (c) 90 (d) 33
  5. 5.The numbers 3 to 11 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) 7 (c) 24 (d) 63
  6. 6.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) 98 (c) 107 (d) 116
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  8. 8.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 394 (d) 393
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 7 (b) 8 (c) 3 (d) 9
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  13. 13.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 82 (c) 72 (d) 90
  14. 14.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) 21 (d) 18
  15. 15.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 77 (c) 78 (d) 86
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  17. 17.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) 51 (b) 144 (c) 16 (d) 48
  18. 18.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 351 (c) 234 (d) 243
  19. 19.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
  20. 20.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 249 (c) 244 (d) 259
  21. 21.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) 69 (b) 23 (c) 72 (d) 207
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  24. 24.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 163 (c) 154 (d) 164
  25. 25.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) 618 (c) 628 (d) 627
  26. 26.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) 162 (b) 54 (c) 57 (d) 18
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 6 (c) 3 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  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) 42 (b) 14 (c) 126 (d) 45
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 11 (b) 10 (c) 8 (d) 9
  31. 31.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 418 (c) 510 (d) 519
  32. 32.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 31 (c) 22 (d) 32
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  34. 34.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 161 (c) 162 (d) 170
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  36. 36.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
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  38. 38.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) 66 (c) 22 (d) 198
  39. 39.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 318 (c) 284 (d) 319
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 10 (d) 3

Answer key

  1. 3
  2. 24
  3. 516
  4. 30
  5. 21
  6. 107
  7. 5
  8. 393
  9. 9
  10. 8
  11. 3
  12. 20
  13. 81
  14. 18
  15. 77
  16. 6
  17. 48
  18. 243
  19. 15
  20. 258
  21. 69
  22. 6
  23. 19
  24. 163
  25. 627
  26. 54
  27. 5
  28. 2
  29. 42
  30. 10
  31. 519
  32. 31
  33. 5
  34. 161
  35. 7
  36. 45
  37. 4
  38. 66
  39. 318
  40. 10

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