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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 925 · 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 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 106 (c) 88 (d) 97
  2. 2.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) 7 (b) 63 (c) 24 (d) 21
  3. 3.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) 17 (d) 54
  4. 4.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) 57 (c) 171 (d) 19
  5. 5.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 18 (d) 57
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 2 (d) 4
  7. 7.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) 135 (b) 48 (c) 45 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  10. 10.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) 108 (c) 12 (d) 39
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 9 (c) 19 (d) 20
  12. 12.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 343 (c) 342 (d) 333
  13. 13.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 627 (c) 618 (d) 628
  14. 14.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 31 (c) 22 (d) 32
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  17. 17.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 60 (d) 180
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 2 (d) 4
  19. 19.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 552 (c) 440 (d) 543
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 20 (d) 21
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 5 (d) 4
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  29. 29.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 243 (c) 253 (d) 240
  30. 30.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 482 (c) 616 (d) 606
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 17 (c) 8 (d) 18
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 16 (d) 6
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  34. 34.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) 558 (d) 549
  35. 35.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 116 (c) 124 (d) 106
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 20 (d) 9
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
  39. 39.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 60 (c) 50 (d) 59
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 16 (d) 17

Answer key

  1. 97
  2. 21
  3. 51
  4. 57
  5. 54
  6. 3
  7. 45
  8. 5
  9. 4
  10. 36
  11. 19
  12. 342
  13. 627
  14. 31
  15. 2
  16. 3
  17. 60
  18. 4
  19. 552
  20. 4
  21. 20
  22. 3
  23. 19
  24. 17
  25. 17
  26. 5
  27. 19
  28. 9
  29. 252
  30. 615
  31. 18
  32. 17
  33. 7
  34. 558
  35. 115
  36. 20
  37. 7
  38. 3
  39. 59
  40. 17

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