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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 922 · 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 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) 6 (b) 54 (c) 21 (d) 18
  2. 2.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) 69 (b) 23 (c) 207 (d) 72
  3. 3.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) 12 (c) 108 (d) 36
  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) 276 (b) 262 (c) 285 (d) 286
  5. 5.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 80 (c) 62 (d) 72
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 13 (b) 14 (c) 4 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  12. 12.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 167 (c) 158 (d) 168
  13. 13.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) 90 (c) 33 (d) 10
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 5 (d) 6
  15. 15.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) 22 (b) 198 (c) 66 (d) 69
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 17 (b) 18 (c) 16 (d) 7
  17. 17.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 381 (d) 326
  18. 18.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 124 (d) 123
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  20. 20.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) 180 (b) 63 (c) 60 (d) 20
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
  22. 22.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 390 (d) 338
  23. 23.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 624 (c) 494 (d) 634
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 4 (d) 2
  25. 25.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 399 (c) 408 (d) 344
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 6 (d) 9
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 8 (d) 20
  28. 28.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 100 (c) 118 (d) 109
  29. 29.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) 19 (b) 60 (c) 57 (d) 171
  30. 30.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 486 (c) 496 (d) 495
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  32. 32.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
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 3 (b) 2 (c) 4 (d) 5
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 20 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  37. 37.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) 39 (b) 13 (c) 117 (d) 42
  38. 38.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) 21 (b) 7 (c) 63 (d) 24
  39. 39.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) 24 (c) 75 (d) 72
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4

Answer key

  1. 18
  2. 69
  3. 36
  4. 285
  5. 71
  6. 2
  7. 14
  8. 8
  9. 20
  10. 5
  11. 3
  12. 167
  13. 30
  14. 6
  15. 66
  16. 17
  17. 381
  18. 123
  19. 20
  20. 60
  21. 3
  22. 399
  23. 633
  24. 4
  25. 408
  26. 8
  27. 19
  28. 109
  29. 57
  30. 495
  31. 9
  32. 24
  33. 7
  34. 4
  35. 19
  36. 9
  37. 39
  38. 21
  39. 72
  40. 4

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