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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 231 · 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 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) 36 (d) 33
  2. 2.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) 45 (b) 18 (c) 15 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  4. 4.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 372 (c) 363 (d) 320
  5. 5.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) 21 (c) 7 (d) 63
  6. 6.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) 27 (b) 8 (c) 24 (d) 72
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 21 (b) 9 (c) 20 (d) 19
  8. 8.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) 69 (b) 66 (c) 198 (d) 22
  9. 9.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) 171 (b) 19 (c) 57 (d) 60
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 15 (c) 14 (d) 13
  12. 12.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) 18 (c) 6 (d) 54
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 9 (d) 19
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
  15. 15.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 402 (d) 486
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  17. 17.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 357 (c) 367 (d) 316
  18. 18.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 361 (c) 351 (d) 312
  19. 19.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) 63 (b) 20 (c) 60 (d) 180
  20. 20.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 188 (c) 178 (d) 196
  21. 21.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 45 (c) 46 (d) 36
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  23. 23.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) 42 (b) 117 (c) 13 (d) 39
  24. 24.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 490 (c) 398 (d) 489
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  26. 26.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) 14 (b) 126 (c) 42 (d) 45
  27. 27.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 198 (c) 199 (d) 189
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 4 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  30. 30.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 51 (b) 52 (c) 60 (d) 42
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 17 (d) 19
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 6 (b) 9 (c) 8 (d) 4
  34. 34.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 74 (c) 83 (d) 92
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 17 (c) 18 (d) 8
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 20 (d) 9
  37. 37.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) 36 (b) 12 (c) 39 (d) 108
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 17 (d) 7
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 10 (b) 9 (c) 3 (d) 11
  40. 40.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 561 (d) 446

Answer key

  1. 33
  2. 15
  3. 5
  4. 372
  5. 21
  6. 24
  7. 20
  8. 66
  9. 57
  10. 2
  11. 14
  12. 18
  13. 19
  14. 3
  15. 495
  16. 7
  17. 366
  18. 360
  19. 60
  20. 187
  21. 45
  22. 20
  23. 39
  24. 489
  25. 2
  26. 42
  27. 198
  28. 3
  29. 8
  30. 51
  31. 5
  32. 18
  33. 8
  34. 83
  35. 18
  36. 20
  37. 36
  38. 17
  39. 10
  40. 561

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