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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 135 · 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 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) 21 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
  5. 5.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) 6 (c) 54 (d) 18
  6. 6.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 490 (c) 480 (d) 489
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  8. 8.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) 19 (c) 171 (d) 57
  9. 9.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 273 (c) 264 (d) 274
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 1
  11. 11.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) 126 (b) 45 (c) 42 (d) 14
  12. 12.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 120 (c) 102 (d) 112
  13. 13.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) 36 (b) 11 (c) 33 (d) 99
  14. 14.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 109 (c) 118 (d) 110
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 18
  16. 16.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 370 (c) 369 (d) 360
  17. 17.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 559 (c) 549 (d) 558
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 9 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 14 (b) 16 (c) 5 (d) 15
  21. 21.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 381 (c) 391 (d) 390
  22. 22.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 161 (b) 162 (c) 152 (d) 170
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 15 (d) 14
  24. 24.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 94 (d) 86
  25. 25.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 76 (c) 58 (d) 68
  26. 26.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 369 (c) 379 (d) 378
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 4 (c) 15 (d) 14
  30. 30.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 174 (c) 156 (d) 166
  31. 31.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) 23 (b) 207 (c) 72 (d) 69
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  35. 35.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 414 (c) 405 (d) 348
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  37. 37.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 522 (c) 420 (d) 513
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 17 (d) 19
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 16 (d) 18

Answer key

  1. 21
  2. 7
  3. 4
  4. 17
  5. 18
  6. 489
  7. 3
  8. 57
  9. 273
  10. 3
  11. 42
  12. 111
  13. 33
  14. 109
  15. 19
  16. 369
  17. 558
  18. 9
  19. 9
  20. 15
  21. 390
  22. 161
  23. 15
  24. 85
  25. 67
  26. 378
  27. 5
  28. 8
  29. 14
  30. 165
  31. 69
  32. 7
  33. 19
  34. 2
  35. 414
  36. 8
  37. 522
  38. 18
  39. 4
  40. 17

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