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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 505 · 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 4? (a) 4 (b) 10 (c) 5 (d) 3
  2. 2.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) 48 (c) 15 (d) 135
  3. 3.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 42 (d) 39
  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) 63 (b) 66 (c) 21 (d) 189
  5. 5.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) 144 (d) 51
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  7. 7.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 552 (c) 561 (d) 446
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  9. 9.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 77 (d) 78
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 6 (d) 16
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 3 (b) 4 (c) 2 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  14. 14.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) 57 (b) 60 (c) 171 (d) 19
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 4 (b) 5 (c) 7 (d) 6
  16. 16.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) 162 (b) 18 (c) 54 (d) 57
  17. 17.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 428 (c) 535 (d) 525
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  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) 288 (b) 324 (c) 315 (d) 325
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 5 (d) 4
  22. 22.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) 11 (c) 33 (d) 36
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 17 (b) 16 (c) 5 (d) 15
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 6 (b) 16 (c) 18 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 15 (d) 14
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 5 (b) 3 (c) 6 (d) 4
  29. 29.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 243 (d) 351
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 14 (d) 13
  31. 31.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 76 (c) 75 (d) 66
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
  33. 33.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 391 (c) 390 (d) 381
  34. 34.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 142 (c) 132 (d) 141
  35. 35.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) 216 (b) 72 (c) 24 (d) 75
  36. 36.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 52 (d) 60
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 19 (b) 21 (c) 9 (d) 20
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 18 (d) 20
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 18 (d) 8

Answer key

  1. 4
  2. 45
  3. 39
  4. 63
  5. 48
  6. 5
  7. 561
  8. 8
  9. 77
  10. 9
  11. 17
  12. 4
  13. 6
  14. 57
  15. 6
  16. 54
  17. 534
  18. 4
  19. 324
  20. 2
  21. 4
  22. 33
  23. 7
  24. 16
  25. 17
  26. 8
  27. 14
  28. 5
  29. 243
  30. 14
  31. 75
  32. 3
  33. 390
  34. 141
  35. 72
  36. 51
  37. 20
  38. 19
  39. 3
  40. 19

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