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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 323 · 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.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 374 (c) 444 (d) 453
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 7 (b) 8 (c) 9 (d) 6
  3. 3.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) 69 (c) 70 (d) 60
  4. 4.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 238 (d) 249
  5. 5.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 296 (c) 337 (d) 336
  6. 6.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 442 (c) 555 (d) 556
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 4 (d) 15
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 4 (b) 5 (c) 6 (d) 3
  9. 9.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 14 (d) 3
  11. 11.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) 16 (b) 144 (c) 51 (d) 48
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 20 (b) 21 (c) 19 (d) 9
  14. 14.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 116 (c) 106 (d) 115
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  16. 16.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  17. 17.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) 18 (b) 6 (c) 21 (d) 54
  18. 18.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) 42 (c) 13 (d) 117
  19. 19.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 334 (c) 393 (d) 394
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 5 (d) 7
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 8 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 19 (d) 17
  25. 25.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) 21 (c) 63 (d) 7
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  27. 27.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) 36 (b) 11 (c) 99 (d) 33
  28. 28.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 354 (c) 363 (d) 364
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 3 (b) 2 (c) 1 (d) 4
  31. 31.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) 27 (c) 8 (d) 24
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  33. 33.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 180 (d) 190
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 5 (d) 16
  36. 36.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 236 (c) 237 (d) 247
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 19 (d) 8
  38. 38.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) 36 (c) 12 (d) 108
  39. 39.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 68 (c) 50 (d) 59
  40. 40.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) 10 (b) 33 (c) 30 (d) 90

Answer key

  1. 453
  2. 8
  3. 69
  4. 249
  5. 336
  6. 555
  7. 15
  8. 5
  9. 6
  10. 14
  11. 48
  12. 4
  13. 20
  14. 115
  15. 2
  16. 3
  17. 18
  18. 39
  19. 393
  20. 8
  21. 7
  22. 19
  23. 5
  24. 18
  25. 21
  26. 2
  27. 33
  28. 363
  29. 5
  30. 3
  31. 24
  32. 3
  33. 189
  34. 7
  35. 16
  36. 246
  37. 19
  38. 36
  39. 59
  40. 30

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