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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 946 · 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.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 37 (c) 28 (d) 38
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 2 (d) 3
  3. 3.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 309 (c) 278 (d) 310
  4. 4.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 276 (c) 286 (d) 262
  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) 16 (b) 144 (c) 48 (d) 51
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 8 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  9. 9.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 354 (c) 308 (d) 355
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 18 (d) 19
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 5 (b) 6 (c) 3 (d) 4
  12. 12.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) 13 (b) 39 (c) 42 (d) 117
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  14. 14.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) 15 (b) 45 (c) 48 (d) 135
  15. 15.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 370 (c) 318 (d) 360
  16. 16.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) 63 (b) 7 (c) 24 (d) 21
  17. 17.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) 54 (b) 6 (c) 21 (d) 18
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 18 (d) 17
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
  20. 20.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 149 (c) 150 (d) 158
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  22. 22.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) 9 (b) 30 (c) 81 (d) 27
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 19 (d) 17
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  26. 26.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 556 (c) 546 (d) 555
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  28. 28.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 330 (c) 340 (d) 339
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 19 (d) 17
  31. 31.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 82 (c) 81 (d) 90
  32. 32.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) 33 (b) 90 (c) 30 (d) 10
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  34. 34.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
  35. 35.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
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 6 (c) 8 (d) 7
  37. 37.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) 75 (b) 216 (c) 24 (d) 72
  38. 38.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
  39. 39.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
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8

Answer key

  1. 37
  2. 4
  3. 309
  4. 285
  5. 48
  6. 19
  7. 3
  8. 6
  9. 354
  10. 19
  11. 5
  12. 39
  13. 3
  14. 45
  15. 369
  16. 21
  17. 18
  18. 17
  19. 20
  20. 149
  21. 5
  22. 27
  23. 18
  24. 15
  25. 2
  26. 555
  27. 8
  28. 339
  29. 7
  30. 18
  31. 81
  32. 30
  33. 5
  34. 159
  35. 36
  36. 7
  37. 72
  38. 63
  39. 79
  40. 9

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