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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 508 · 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 9? (a) 9 (b) 8 (c) 10 (d) 11
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  3. 3.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) 20 (b) 63 (c) 60 (d) 180
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 13 (d) 15
  5. 5.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) 24 (b) 8 (c) 27 (d) 72
  6. 6.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) 525 (c) 535 (d) 428
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  8. 8.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 334 (c) 384 (d) 393
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 8 (b) 9 (c) 10 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  13. 13.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) 42 (b) 14 (c) 45 (d) 126
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 2 (b) 4 (c) 3 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  18. 18.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) 21 (c) 66 (d) 189
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 5 (b) 4 (c) 6 (d) 3
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 3 (d) 5
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 5 (d) 7
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 6 (d) 7
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 5 (b) 6 (c) 4 (d) 7
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 16 (d) 4
  26. 26.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
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 4 (d) 1
  29. 29.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 370 (c) 369 (d) 318
  30. 30.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 93 (d) 94
  31. 31.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) 72 (b) 69 (c) 207 (d) 23
  32. 32.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) 39 (b) 36 (c) 12 (d) 108
  33. 33.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 163 (c) 164 (d) 154
  34. 34.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) 39 (d) 42
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 19 (d) 8
  36. 36.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 444 (c) 374 (d) 454
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 20 (b) 18 (c) 19 (d) 9
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  39. 39.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 30 (d) 9
  40. 40.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 184 (c) 166 (d) 176

Answer key

  1. 9
  2. 2
  3. 60
  4. 14
  5. 24
  6. 534
  7. 6
  8. 393
  9. 6
  10. 5
  11. 9
  12. 4
  13. 42
  14. 3
  15. 4
  16. 4
  17. 3
  18. 63
  19. 5
  20. 4
  21. 3
  22. 6
  23. 7
  24. 6
  25. 15
  26. 324
  27. 4
  28. 3
  29. 369
  30. 93
  31. 69
  32. 36
  33. 163
  34. 39
  35. 19
  36. 453
  37. 19
  38. 19
  39. 27
  40. 175

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