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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 370 · 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 9? (a) 9 (b) 10 (c) 11 (d) 8
  2. 2.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 91 (d) 100
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 10 (b) 12 (c) 4 (d) 11
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  5. 5.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 469 (d) 468
  6. 6.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 309 (c) 310 (d) 300
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  9. 9.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) 72 (b) 69 (c) 23 (d) 207
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 13 (c) 14 (d) 15
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 5 (d) 4
  12. 12.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 74 (c) 56 (d) 65
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 17 (d) 5
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 16 (d) 17
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  16. 16.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) 78 (d) 60
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 7 (d) 16
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  19. 19.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) 45 (b) 135 (c) 48 (d) 15
  20. 20.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) 75 (b) 24 (c) 216 (d) 72
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 17 (c) 16 (d) 15
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 5 (d) 6
  25. 25.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) 8 (c) 24 (d) 27
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 13 (c) 14 (d) 3
  27. 27.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 438 (c) 540 (d) 549
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 3 (d) 4
  29. 29.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 158 (c) 149 (d) 150
  30. 30.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 205 (c) 208 (d) 204
  31. 31.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 134 (d) 125
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 9 (d) 20
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 9 (d) 21
  34. 34.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 244 (c) 259 (d) 249
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 5 (d) 17
  36. 36.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 256 (c) 276 (d) 277
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 6 (c) 7 (d) 5
  38. 38.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 153 (c) 154 (d) 162
  39. 39.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 346 (c) 302 (d) 336
  40. 40.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) 99 (d) 36

Answer key

  1. 9
  2. 91
  3. 11
  4. 8
  5. 468
  6. 309
  7. 20
  8. 6
  9. 69
  10. 14
  11. 4
  12. 65
  13. 16
  14. 17
  15. 9
  16. 69
  17. 17
  18. 5
  19. 45
  20. 72
  21. 7
  22. 16
  23. 4
  24. 5
  25. 24
  26. 13
  27. 549
  28. 3
  29. 149
  30. 204
  31. 125
  32. 19
  33. 20
  34. 258
  35. 16
  36. 276
  37. 7
  38. 153
  39. 345
  40. 33

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