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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 813 · 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) 7 (c) 8 (d) 10
  2. 2.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) 19 (b) 171 (c) 60 (d) 57
  3. 3.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 300 (c) 278 (d) 310
  4. 4.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) 17 (b) 54 (c) 51 (d) 153
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  8. 8.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 615 (c) 616 (d) 482
  9. 9.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 254 (c) 264 (d) 273
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 14 (d) 15
  11. 11.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 379 (c) 378 (d) 369
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  13. 13.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 546 (c) 537 (d) 436
  14. 14.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) 24 (c) 63 (d) 7
  15. 15.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) 168 (c) 158 (d) 176
  16. 16.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) 24 (b) 75 (c) 216 (d) 72
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 7 (d) 6
  19. 19.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 541 (d) 540
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 17 (d) 7
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 5 (b) 7 (c) 4 (d) 6
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 14 (b) 13 (c) 3 (d) 15
  24. 24.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) 90 (b) 30 (c) 33 (d) 10
  25. 25.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 128 (c) 137 (d) 138
  26. 26.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 570 (d) 579
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 5 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  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) 66 (b) 63 (c) 189 (d) 21
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 16 (c) 5 (d) 15
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 18 (d) 17
  35. 35.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 210 (d) 211
  36. 36.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) 9 (b) 30 (c) 81 (d) 27
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 7 (d) 17
  38. 38.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 144 (c) 152 (d) 143
  39. 39.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 448 (c) 447 (d) 370
  40. 40.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 24 (c) 33 (d) 42

Answer key

  1. 7
  2. 57
  3. 309
  4. 51
  5. 2
  6. 6
  7. 9
  8. 615
  9. 273
  10. 14
  11. 378
  12. 18
  13. 546
  14. 21
  15. 167
  16. 72
  17. 19
  18. 6
  19. 540
  20. 17
  21. 19
  22. 6
  23. 14
  24. 30
  25. 137
  26. 579
  27. 4
  28. 4
  29. 8
  30. 63
  31. 5
  32. 15
  33. 16
  34. 17
  35. 210
  36. 27
  37. 18
  38. 143
  39. 447
  40. 33

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