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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 903 · 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 6 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 18 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  4. 4.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 177 (b) 186 (c) 178 (d) 168
  5. 5.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 339 (c) 304 (d) 348
  6. 6.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 388 (c) 475 (d) 474
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  9. 9.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) 27 (b) 8 (c) 24 (d) 72
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 4 (d) 3
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 4 (c) 5 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  15. 15.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 406 (d) 501
  16. 16.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 19 (d) 7
  18. 18.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) 81 (b) 9 (c) 30 (d) 27
  19. 19.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 405 (c) 415 (d) 348
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  21. 21.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) 7 (d) 63
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 9 (d) 10
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 16 (d) 4
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 18 (d) 7
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 21 (d) 19
  26. 26.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 158 (c) 176 (d) 168
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 14 (d) 4
  28. 28.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) 48 (c) 16 (d) 51
  29. 29.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  30. 30.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) 189 (b) 21 (c) 63 (d) 66
  31. 31.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 48 (c) 40 (d) 30
  32. 32.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 202 (c) 196 (d) 186
  33. 33.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) 171 (b) 57 (c) 19 (d) 60
  34. 34.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 264 (c) 274 (d) 273
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 10 (b) 4 (c) 11 (d) 9
  36. 36.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 540 (c) 432 (d) 531
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 17 (d) 6
  38. 38.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 601 (c) 600 (d) 591
  39. 39.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  40. 40.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 18 (d) 54

Answer key

  1. 19
  2. 9
  3. 6
  4. 177
  5. 348
  6. 474
  7. 3
  8. 17
  9. 24
  10. 20
  11. 8
  12. 3
  13. 5
  14. 9
  15. 501
  16. 60
  17. 18
  18. 27
  19. 414
  20. 5
  21. 21
  22. 9
  23. 15
  24. 18
  25. 20
  26. 167
  27. 15
  28. 48
  29. 5
  30. 63
  31. 39
  32. 195
  33. 57
  34. 273
  35. 10
  36. 540
  37. 17
  38. 600
  39. 3
  40. 54

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