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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 69 · 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.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 19 (d) 18
  2. 2.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) 162 (b) 54 (c) 57 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 17 (d) 16
  5. 5.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 181 (c) 182 (d) 190
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  7. 7.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 100 (c) 110 (d) 118
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 5 (b) 7 (c) 6 (d) 8
  9. 9.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) 21 (b) 189 (c) 66 (d) 63
  10. 10.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 40 (c) 30 (d) 48
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 18 (d) 17
  13. 13.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 284 (c) 309 (d) 318
  14. 14.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 549 (c) 444 (d) 559
  15. 15.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 500 (c) 643 (d) 633
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  17. 17.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) 24 (c) 8 (d) 72
  18. 18.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
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 4 (b) 2 (c) 3 (d) 5
  21. 21.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 199 (c) 189 (d) 204
  22. 22.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 373 (c) 320 (d) 372
  23. 23.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) 75 (c) 216 (d) 72
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 3 (d) 4
  25. 25.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 592 (c) 591 (d) 466
  26. 26.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) 117 (b) 42 (c) 13 (d) 39
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 18 (d) 7
  30. 30.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 568 (c) 450 (d) 558
  31. 31.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 346 (c) 402 (d) 412
  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) 57 (b) 19 (c) 60 (d) 171
  33. 33.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
  34. 34.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  35. 35.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 291 (c) 266 (d) 282
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  38. 38.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 441 (d) 442
  39. 39.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 153 (d) 51
  40. 40.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) 60 (b) 20 (c) 180 (d) 63

Answer key

  1. 18
  2. 54
  3. 5
  4. 17
  5. 181
  6. 6
  7. 109
  8. 7
  9. 63
  10. 39
  11. 4
  12. 17
  13. 318
  14. 558
  15. 642
  16. 2
  17. 24
  18. 27
  19. 3
  20. 4
  21. 198
  22. 372
  23. 72
  24. 4
  25. 591
  26. 39
  27. 8
  28. 5
  29. 18
  30. 567
  31. 411
  32. 57
  33. 36
  34. 4
  35. 291
  36. 7
  37. 8
  38. 441
  39. 51
  40. 60

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