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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 975 · 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 4 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 16 (d) 17
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 3 (d) 4
  3. 3.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) 166 (c) 174 (d) 156
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18
  5. 5.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) 18 (c) 5 (d) 15
  6. 6.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 213 (c) 321 (d) 214
  7. 7.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
  8. 8.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) 14 (d) 42
  9. 9.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 459 (d) 460
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  11. 11.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
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 16 (c) 17 (d) 7
  14. 14.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
  15. 15.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 606 (c) 597 (d) 607
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 4 (c) 6 (d) 5
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 17 (d) 18
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 18 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 7 (b) 19 (c) 18 (d) 17
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 18 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  26. 26.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
  27. 27.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) 48 (b) 51 (c) 16 (d) 144
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 18 (d) 8
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 7 (c) 6 (d) 4
  30. 30.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 435 (c) 368 (d) 444
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 14 (d) 15
  36. 36.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 260 (d) 282
  37. 37.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 54 (c) 45 (d) 36
  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) 66 (b) 69 (c) 22 (d) 198
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  40. 40.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 56 (c) 48 (d) 47

Answer key

  1. 17
  2. 4
  3. 165
  4. 18
  5. 15
  6. 213
  7. 39
  8. 42
  9. 459
  10. 6
  11. 24
  12. 2
  13. 17
  14. 258
  15. 606
  16. 6
  17. 18
  18. 17
  19. 6
  20. 5
  21. 20
  22. 3
  23. 18
  24. 18
  25. 2
  26. 489
  27. 48
  28. 18
  29. 6
  30. 444
  31. 3
  32. 8
  33. 18
  34. 9
  35. 14
  36. 282
  37. 45
  38. 66
  39. 7
  40. 47

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