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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 259 · 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 6 written when you write all the numbers from 1 to 96? (a) 20 (b) 19 (c) 9 (d) 21
  2. 2.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 79 (d) 88
  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) 51 (b) 153 (c) 17 (d) 54
  4. 4.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 144 (c) 153 (d) 162
  5. 5.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) 48 (b) 15 (c) 45 (d) 135
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 4 (b) 15 (c) 16 (d) 14
  8. 8.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 385 (c) 375 (d) 384
  9. 9.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 101 (c) 110 (d) 102
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  11. 11.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) 69 (b) 207 (c) 72 (d) 23
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 18 (d) 20
  14. 14.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) 144 (b) 48 (c) 16 (d) 51
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 20
  16. 16.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) 99 (d) 33
  17. 17.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) 379 (c) 378 (d) 369
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  20. 20.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) 54 (c) 6 (d) 18
  21. 21.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 205 (c) 195 (d) 204
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  23. 23.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 104 (c) 112 (d) 103
  24. 24.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 414 (c) 504 (d) 514
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 3 (d) 10
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 15 (b) 16 (c) 17 (d) 5
  27. 27.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) 543 (c) 552 (d) 440
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 6 (d) 16
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 8 (c) 19 (d) 18
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9
  33. 33.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 430 (c) 429 (d) 358
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 17 (b) 18 (c) 7 (d) 16
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 16 (b) 18 (c) 19 (d) 9
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  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) 22 (c) 198 (d) 69
  39. 39.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) 108 (b) 39 (c) 36 (d) 12
  40. 40.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

Answer key

  1. 20
  2. 79
  3. 51
  4. 153
  5. 45
  6. 6
  7. 15
  8. 384
  9. 101
  10. 5
  11. 69
  12. 7
  13. 19
  14. 48
  15. 19
  16. 33
  17. 378
  18. 4
  19. 3
  20. 18
  21. 204
  22. 2
  23. 103
  24. 513
  25. 10
  26. 16
  27. 552
  28. 16
  29. 5
  30. 8
  31. 19
  32. 19
  33. 429
  34. 3
  35. 17
  36. 18
  37. 8
  38. 66
  39. 36
  40. 42

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