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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 103 · 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.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 252 (d) 253
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  3. 3.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) 27 (c) 8 (d) 24
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 4 (d) 16
  5. 5.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 412 (d) 511
  6. 6.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 14 (c) 45 (d) 126
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 17 (d) 7
  9. 9.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
  10. 10.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 189 (c) 198 (d) 204
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  12. 12.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) 33 (c) 10 (d) 30
  13. 13.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
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  15. 15.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 206 (c) 202 (d) 192
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 7 (b) 6 (c) 8 (d) 5
  17. 17.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 514 (c) 414 (d) 504
  18. 18.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 327 (c) 318 (d) 290
  19. 19.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 45 (d) 15
  20. 20.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) 63 (b) 24 (c) 7 (d) 21
  21. 21.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) 57 (c) 171 (d) 19
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 17 (c) 18 (d) 7
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 7 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 15 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  27. 27.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 504 (d) 495
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  29. 29.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) 180 (b) 20 (c) 60 (d) 63
  30. 30.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 603 (d) 612
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 8 (b) 7 (c) 5 (d) 6
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 16 (d) 18
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 3 (c) 5 (d) 4
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 15 (d) 5
  35. 35.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  36. 36.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) 21 (b) 66 (c) 189 (d) 63
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 1
  38. 38.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 224 (c) 219 (d) 228
  39. 39.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 274 (d) 264
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6

Answer key

  1. 252
  2. 6
  3. 24
  4. 15
  5. 510
  6. 42
  7. 4
  8. 18
  9. 72
  10. 198
  11. 4
  12. 30
  13. 69
  14. 8
  15. 201
  16. 7
  17. 513
  18. 327
  19. 15
  20. 21
  21. 57
  22. 18
  23. 6
  24. 3
  25. 14
  26. 7
  27. 504
  28. 5
  29. 60
  30. 612
  31. 7
  32. 17
  33. 4
  34. 16
  35. 2
  36. 63
  37. 3
  38. 228
  39. 273
  40. 5

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