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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 98 · 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 two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 5 (d) 6
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 7 (b) 14 (c) 13 (d) 11
  4. 4.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 218 (c) 220 (d) 219
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 17 (d) 18
  6. 6.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) 153 (b) 17 (c) 54 (d) 51
  7. 7.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 445 (c) 444 (d) 435
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  10. 10.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 282 (c) 283 (d) 260
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  12. 12.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 326 (c) 382 (d) 381
  13. 13.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 60 (d) 78
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 4 (d) 5
  15. 15.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
  16. 16.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 507 (c) 498 (d) 508
  17. 17.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 104 (d) 114
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 6 (d) 5
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 7 (b) 12 (c) 13 (d) 10
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  23. 23.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) 30 (c) 90 (d) 33
  24. 24.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) 12 (b) 36 (c) 108 (d) 39
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 4 (d) 14
  28. 28.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 14 (c) 13 (d) 12
  32. 32.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 144 (c) 136 (d) 135
  33. 33.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 270 (d) 258
  34. 34.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 41 (c) 42 (d) 50
  35. 35.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 272 (c) 291 (d) 300
  36. 36.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 351 (c) 352 (d) 306
  37. 37.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 639 (c) 498 (d) 630
  38. 38.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 321 (d) 322
  39. 39.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) 21 (c) 63 (d) 24
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 3 (d) 14

Answer key

  1. 5
  2. 5
  3. 13
  4. 219
  5. 17
  6. 51
  7. 444
  8. 6
  9. 3
  10. 282
  11. 9
  12. 381
  13. 69
  14. 4
  15. 33
  16. 507
  17. 113
  18. 9
  19. 7
  20. 20
  21. 12
  22. 8
  23. 30
  24. 36
  25. 2
  26. 3
  27. 15
  28. 141
  29. 20
  30. 2
  31. 13
  32. 135
  33. 279
  34. 41
  35. 300
  36. 351
  37. 639
  38. 321
  39. 21
  40. 14

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