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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 637 · 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 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) 30 (c) 10 (d) 90
  2. 2.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) 24 (b) 72 (c) 216 (d) 75
  3. 3.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 183 (c) 192 (d) 184
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  5. 5.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) 360 (c) 370 (d) 318
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 7 (b) 16 (c) 17 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  9. 9.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) 126 (b) 14 (c) 42 (d) 45
  10. 10.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
  11. 11.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 458 (c) 579 (d) 570
  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) 6 (b) 54 (c) 21 (d) 18
  13. 13.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 356 (c) 427 (d) 426
  14. 14.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) 11 (b) 33 (c) 36 (d) 99
  15. 15.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 465 (c) 382 (d) 456
  16. 16.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 168 (d) 158
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 5 (d) 4
  20. 20.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 180 (d) 171
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 16 (d) 14
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 2 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
  27. 27.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) 135 (b) 15 (c) 48 (d) 45
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 18 (d) 17
  29. 29.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 134 (c) 142 (d) 133
  30. 30.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) 7 (b) 63 (c) 24 (d) 21
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  32. 32.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) 171 (d) 57
  33. 33.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 252 (c) 240 (d) 243
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 18 (d) 19
  37. 37.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 57 (d) 58
  38. 38.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 531 (c) 532 (d) 426
  39. 39.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 76 (c) 94 (d) 85
  40. 40.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 392 (c) 471 (d) 481

Answer key

  1. 30
  2. 72
  3. 183
  4. 2
  5. 369
  6. 5
  7. 17
  8. 5
  9. 42
  10. 63
  11. 579
  12. 18
  13. 426
  14. 33
  15. 465
  16. 167
  17. 4
  18. 7
  19. 4
  20. 171
  21. 18
  22. 4
  23. 15
  24. 4
  25. 5
  26. 17
  27. 45
  28. 17
  29. 133
  30. 21
  31. 8
  32. 57
  33. 252
  34. 9
  35. 3
  36. 19
  37. 57
  38. 531
  39. 85
  40. 480

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