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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 798 · 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 7? (a) 6 (b) 8 (c) 7 (d) 10
  2. 2.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 128 (c) 110 (d) 119
  3. 3.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 438 (c) 448 (d) 370
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  6. 6.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 7 (b) 8 (c) 9 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 14 (d) 13
  11. 11.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 297 (c) 288 (d) 270
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  13. 13.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) 144 (b) 16 (c) 48 (d) 51
  14. 14.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 125 (b) 134 (c) 126 (d) 116
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  16. 16.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) 99 (b) 33 (c) 36 (d) 11
  17. 17.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) 27 (b) 9 (c) 30 (d) 81
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 4 (d) 6
  20. 20.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) 60 (b) 19 (c) 57 (d) 171
  21. 21.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) 51 (b) 17 (c) 54 (d) 153
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 4 (d) 2
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 10 (c) 3 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  25. 25.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 558 (c) 568 (d) 567
  26. 26.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 546 (c) 556 (d) 442
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 2 (d) 3
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 14 (d) 15
  31. 31.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 140 (c) 131 (d) 122
  32. 32.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) 21 (b) 7 (c) 63 (d) 24
  33. 33.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) 90 (d) 30
  34. 34.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 357 (d) 366
  35. 35.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 306 (c) 316 (d) 315
  36. 36.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 280 (c) 312 (d) 303
  37. 37.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 550 (c) 438 (d) 549
  38. 38.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 214 (c) 213 (d) 321
  39. 39.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 375 (c) 322 (d) 366
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2

Answer key

  1. 7
  2. 119
  3. 447
  4. 4
  5. 4
  6. 177
  7. 5
  8. 8
  9. 4
  10. 14
  11. 297
  12. 6
  13. 48
  14. 125
  15. 3
  16. 33
  17. 27
  18. 9
  19. 5
  20. 57
  21. 51
  22. 3
  23. 9
  24. 3
  25. 567
  26. 555
  27. 2
  28. 8
  29. 3
  30. 15
  31. 131
  32. 21
  33. 30
  34. 366
  35. 315
  36. 312
  37. 549
  38. 213
  39. 375
  40. 4

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