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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 295 · 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.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 303 (c) 313 (d) 280
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 7 (b) 6 (c) 8 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  4. 4.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 276 (c) 256 (d) 277
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 3 (d) 4
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  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) 262 (b) 252 (c) 246 (d) 261
  8. 8.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) 45 (b) 135 (c) 15 (d) 48
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 14 (c) 13 (d) 12
  10. 10.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
  11. 11.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 114 (d) 132
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  13. 13.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 544 (c) 534 (d) 434
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  15. 15.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 71 (c) 72 (d) 62
  16. 16.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) 22 (c) 69 (d) 198
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  21. 21.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 54 (c) 44 (d) 62
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 19 (d) 9
  23. 23.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) 33 (c) 99 (d) 11
  24. 24.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) 51 (c) 54 (d) 17
  25. 25.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 357 (c) 366 (d) 367
  26. 26.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) 18 (b) 5 (c) 15 (d) 45
  27. 27.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) 36 (b) 39 (c) 12 (d) 108
  28. 28.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 553 (c) 440 (d) 543
  29. 29.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 630 (c) 631 (d) 621
  30. 30.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) 207 (b) 72 (c) 23 (d) 69
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 3 (d) 4
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 9 (d) 18
  37. 37.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) 639 (c) 498 (d) 640
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  40. 40.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) 171 (b) 19 (c) 57 (d) 60

Answer key

  1. 312
  2. 7
  3. 7
  4. 276
  5. 5
  6. 5
  7. 261
  8. 45
  9. 13
  10. 24
  11. 123
  12. 6
  13. 543
  14. 2
  15. 71
  16. 66
  17. 7
  18. 4
  19. 2
  20. 20
  21. 53
  22. 20
  23. 33
  24. 51
  25. 366
  26. 15
  27. 36
  28. 552
  29. 630
  30. 69
  31. 16
  32. 9
  33. 19
  34. 4
  35. 3
  36. 19
  37. 639
  38. 18
  39. 3
  40. 57

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