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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 590 · 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 times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  2. 2.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 288 (c) 325 (d) 324
  3. 3.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) 39 (c) 108 (d) 36
  4. 4.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) 170 (c) 162 (d) 161
  5. 5.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  6. 6.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 615 (c) 482 (d) 616
  7. 7.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) 24 (b) 216 (c) 75 (d) 72
  8. 8.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  9. 9.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 408 (c) 417 (d) 350
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  13. 13.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 601 (d) 600
  14. 14.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) 63 (c) 21 (d) 189
  15. 15.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 304 (c) 349 (d) 339
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 19 (d) 7
  17. 17.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 13 (c) 4 (d) 14
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  23. 23.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) 45 (c) 18 (d) 5
  24. 24.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 210 (c) 211 (d) 201
  25. 25.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 176 (c) 175 (d) 184
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 9 (b) 8 (c) 7 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 15 (d) 4
  29. 29.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) 288 (c) 289 (d) 279
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 20
  31. 31.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 627 (c) 636 (d) 637
  32. 32.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) 13 (b) 39 (c) 117 (d) 42
  33. 33.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) 54 (c) 17 (d) 51
  34. 34.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 258 (d) 259
  35. 35.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) 15 (c) 45 (d) 135
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 3 (d) 5
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 4 (b) 6 (c) 5 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  39. 39.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) 24 (b) 63 (c) 7 (d) 21
  40. 40.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 403 (c) 393 (d) 340

Answer key

  1. 19
  2. 324
  3. 36
  4. 161
  5. 4
  6. 615
  7. 72
  8. 3
  9. 417
  10. 2
  11. 18
  12. 6
  13. 600
  14. 63
  15. 348
  16. 18
  17. 53
  18. 9
  19. 14
  20. 2
  21. 8
  22. 5
  23. 15
  24. 210
  25. 175
  26. 9
  27. 4
  28. 15
  29. 288
  30. 19
  31. 636
  32. 39
  33. 51
  34. 258
  35. 45
  36. 5
  37. 5
  38. 7
  39. 21
  40. 402

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