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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 634 · 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) 10 (c) 90 (d) 30
  2. 2.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) 21 (c) 66 (d) 63
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 18 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  5. 5.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) 5 (c) 15 (d) 18
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 2
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  11. 11.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 265 (c) 248 (d) 264
  12. 12.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) 72 (d) 207
  13. 13.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 33 (d) 42
  14. 14.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) 108 (c) 39 (d) 12
  15. 15.The numbers 14 to 22 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) 57 (c) 162 (d) 18
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 7 (b) 9 (c) 6 (d) 8
  17. 17.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 604 (c) 474 (d) 594
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 7 (b) 5 (c) 6 (d) 8
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  21. 21.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) 21 (c) 18 (d) 54
  22. 22.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
  23. 23.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 360 (c) 432 (d) 423
  24. 24.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) 340 (c) 339 (d) 330
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 18 (d) 16
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  27. 27.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) 9 (c) 30 (d) 27
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  29. 29.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 288 (c) 279 (d) 264
  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) 24 (c) 63 (d) 21
  31. 31.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 332 (d) 391
  32. 32.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 350 (c) 418 (d) 408
  33. 33.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 550 (c) 540 (d) 549
  34. 34.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 148 (c) 138 (d) 156
  35. 35.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) 48 (b) 144 (c) 51 (d) 16
  36. 36.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 340 (d) 393
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  38. 38.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 236 (c) 247 (d) 246
  39. 39.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 366 (c) 357 (d) 316
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 6 (d) 5

Answer key

  1. 30
  2. 63
  3. 19
  4. 2
  5. 15
  6. 4
  7. 18
  8. 4
  9. 9
  10. 2
  11. 264
  12. 69
  13. 33
  14. 36
  15. 54
  16. 8
  17. 603
  18. 7
  19. 6
  20. 20
  21. 18
  22. 39
  23. 432
  24. 339
  25. 17
  26. 5
  27. 27
  28. 7
  29. 288
  30. 21
  31. 390
  32. 417
  33. 549
  34. 147
  35. 48
  36. 402
  37. 8
  38. 246
  39. 366
  40. 5

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