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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 451 · 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.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) 16 (c) 51 (d) 48
  2. 2.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 17 (b) 14 (c) 8 (d) 16
  4. 4.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) 189 (b) 66 (c) 63 (d) 21
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  6. 6.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) 24 (b) 7 (c) 63 (d) 21
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 14 (d) 15
  8. 8.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 453 (c) 463 (d) 462
  9. 9.The numbers 20 to 28 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) 216 (c) 75 (d) 24
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 6 (b) 16 (c) 17 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  12. 12.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 513 (c) 522 (d) 523
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  14. 14.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 349 (c) 339 (d) 304
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 19 (d) 21
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  19. 19.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 324 (d) 288
  20. 20.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 160 (d) 152
  21. 21.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) 5 (b) 18 (c) 45 (d) 15
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 12 (b) 13 (c) 4 (d) 11
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 19 (d) 7
  24. 24.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 408 (c) 495 (d) 505
  25. 25.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 13 (b) 3 (c) 15 (d) 14
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  29. 29.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) 17 (b) 54 (c) 51 (d) 153
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 19 (d) 7
  31. 31.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
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 18 (d) 19
  34. 34.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 21 (d) 20
  36. 36.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 163 (c) 154 (d) 172
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 16 (b) 17 (c) 18 (d) 6
  38. 38.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) 30 (b) 10 (c) 90 (d) 33
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 2 (d) 4

Answer key

  1. 48
  2. 3
  3. 16
  4. 63
  5. 6
  6. 21
  7. 15
  8. 462
  9. 72
  10. 17
  11. 5
  12. 522
  13. 19
  14. 348
  15. 20
  16. 3
  17. 9
  18. 7
  19. 324
  20. 151
  21. 15
  22. 12
  23. 18
  24. 504
  25. 8
  26. 14
  27. 4
  28. 2
  29. 51
  30. 18
  31. 18
  32. 3
  33. 19
  34. 4
  35. 20
  36. 163
  37. 17
  38. 30
  39. 9
  40. 4

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