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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 20 · 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 13? (a) 14 (b) 7 (c) 5 (d) 6
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 4 (c) 2 (d) 3
  3. 3.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) 198 (b) 22 (c) 69 (d) 66
  4. 4.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) 18 (b) 21 (c) 6 (d) 54
  5. 5.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) 33 (c) 36 (d) 11
  6. 6.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 86 (c) 85 (d) 76
  7. 7.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 204 (c) 189 (d) 198
  8. 8.The numbers 17 to 25 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) 63 (c) 189 (d) 66
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 8 (c) 9 (d) 11
  11. 11.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 148 (c) 139 (d) 130
  12. 12.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 90 (d) 81
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  14. 14.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 10 (d) 30
  15. 15.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) 18 (c) 57 (d) 162
  16. 16.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
  17. 17.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) 72 (b) 27 (c) 8 (d) 24
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 20 (d) 8
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  20. 20.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 138 (d) 156
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 16 (c) 15 (d) 13
  22. 22.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 72 (d) 54
  23. 23.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 223 (c) 220 (d) 222
  24. 24.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 469 (c) 468 (d) 384
  25. 25.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 76 (c) 84 (d) 66
  26. 26.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 14 (d) 15
  30. 30.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) 16 (c) 51 (d) 144
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  32. 32.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) 45 (b) 14 (c) 126 (d) 42
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 6 (c) 7 (d) 5
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
  35. 35.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 442 (c) 556 (d) 555
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 7 (b) 9 (c) 10 (d) 8
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 9 (b) 21 (c) 19 (d) 20
  39. 39.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 62 (c) 44 (d) 53
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 5 (c) 10 (d) 9

Answer key

  1. 6
  2. 4
  3. 66
  4. 18
  5. 33
  6. 85
  7. 198
  8. 63
  9. 8
  10. 10
  11. 139
  12. 81
  13. 6
  14. 30
  15. 54
  16. 378
  17. 24
  18. 19
  19. 5
  20. 147
  21. 15
  22. 63
  23. 222
  24. 468
  25. 75
  26. 4
  27. 7
  28. 2
  29. 14
  30. 48
  31. 2
  32. 42
  33. 7
  34. 19
  35. 555
  36. 9
  37. 3
  38. 20
  39. 53
  40. 9

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