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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 341 · 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 7? (a) 7 (b) 8 (c) 6 (d) 10
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 9 (d) 20
  3. 3.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 498 (c) 640 (d) 639
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (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) 160 (b) 152 (c) 142 (d) 151
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  7. 7.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 262 (c) 252 (d) 246
  8. 8.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 279 (c) 270 (d) 258
  9. 9.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 62 (c) 80 (d) 71
  10. 10.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) 5 (c) 45 (d) 18
  11. 11.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 238 (d) 249
  12. 12.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) 17 (b) 153 (c) 54 (d) 51
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 21
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  16. 16.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) 108 (b) 39 (c) 36 (d) 12
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 13 (c) 15 (d) 3
  18. 18.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 325 (d) 288
  19. 19.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) 99 (b) 36 (c) 33 (d) 11
  20. 20.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 588 (c) 598 (d) 470
  21. 21.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 213 (c) 220 (d) 223
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 20 (d) 8
  23. 23.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 38 (c) 37 (d) 46
  24. 24.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 390 (c) 399 (d) 400
  25. 25.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 89 (c) 90 (d) 80
  26. 26.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) 78 (c) 86 (d) 77
  27. 27.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) 24 (b) 72 (c) 8 (d) 27
  28. 28.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
  29. 29.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) 72 (b) 24 (c) 216 (d) 75
  30. 30.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 531 (c) 522 (d) 532
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  32. 32.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 100 (c) 109 (d) 118
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 13 (b) 12 (c) 3 (d) 14
  34. 34.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 110 (c) 120 (d) 119
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 15 (c) 14 (d) 13
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 8 (b) 20 (c) 18 (d) 19
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 6
  39. 39.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) 117 (c) 42 (d) 39
  40. 40.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 594 (c) 604 (d) 474

Answer key

  1. 7
  2. 19
  3. 639
  4. 2
  5. 151
  6. 4
  7. 261
  8. 279
  9. 71
  10. 15
  11. 249
  12. 51
  13. 20
  14. 17
  15. 3
  16. 36
  17. 14
  18. 324
  19. 33
  20. 597
  21. 222
  22. 19
  23. 37
  24. 399
  25. 89
  26. 77
  27. 24
  28. 18
  29. 72
  30. 531
  31. 20
  32. 109
  33. 13
  34. 119
  35. 14
  36. 19
  37. 4
  38. 5
  39. 39
  40. 603

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