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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 354 · 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 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 5 (c) 6 (d) 7
  2. 2.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) 408 (c) 344 (d) 399
  3. 3.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) 27 (c) 30 (d) 81
  4. 4.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 250 (c) 268 (d) 258
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 4 (c) 7 (d) 6
  6. 6.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 399 (c) 390 (d) 338
  7. 7.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) 48 (c) 135 (d) 45
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  9. 9.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) 24 (b) 63 (c) 7 (d) 21
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 17 (d) 15
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 15 (c) 13 (d) 16
  13. 13.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 567 (c) 576 (d) 577
  14. 14.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 69 (d) 60
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  16. 16.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) 23 (b) 69 (c) 72 (d) 207
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 15 (d) 13
  20. 20.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) 117 (c) 39 (d) 42
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  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) 372 (b) 363 (c) 373 (d) 320
  23. 23.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 80 (c) 89 (d) 98
  24. 24.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 374 (c) 453 (d) 454
  25. 25.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) 69 (b) 66 (c) 198 (d) 22
  26. 26.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 348 (c) 414 (d) 415
  27. 27.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 433 (c) 423 (d) 432
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 21 (d) 20
  29. 29.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 115 (c) 124 (d) 116
  30. 30.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 217 (d) 216
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 7 (b) 19 (c) 18 (d) 17
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  33. 33.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) 72 (b) 24 (c) 8 (d) 27
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 18 (c) 6 (d) 17
  36. 36.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 448 (c) 564 (d) 555
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 6 (c) 8 (d) 7
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 1
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 6 (c) 3 (d) 4
  40. 40.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) 63 (c) 189 (d) 66

Answer key

  1. 7
  2. 408
  3. 27
  4. 267
  5. 6
  6. 399
  7. 45
  8. 8
  9. 21
  10. 6
  11. 16
  12. 15
  13. 576
  14. 69
  15. 5
  16. 69
  17. 5
  18. 6
  19. 14
  20. 39
  21. 3
  22. 372
  23. 89
  24. 453
  25. 66
  26. 414
  27. 432
  28. 20
  29. 115
  30. 216
  31. 18
  32. 8
  33. 24
  34. 19
  35. 17
  36. 564
  37. 8
  38. 3
  39. 5
  40. 63

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