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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 475 · 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 4? (a) 3 (b) 5 (c) 10 (d) 4
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  3. 3.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 152 (c) 162 (d) 161
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 20 (d) 18
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 17 (d) 18
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 11 (b) 13 (c) 14 (d) 8
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
  10. 10.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) 21 (c) 7 (d) 24
  11. 11.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) 207 (b) 69 (c) 23 (d) 72
  12. 12.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 384 (c) 469 (d) 459
  13. 13.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 54 (d) 21
  14. 14.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) 54 (b) 18 (c) 57 (d) 162
  15. 15.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 580 (c) 458 (d) 570
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 5 (d) 6
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 6 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  19. 19.The numbers 9 to 17 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) 13 (c) 39 (d) 117
  20. 20.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
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  22. 22.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 445 (c) 368 (d) 435
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  25. 25.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 66 (d) 198
  26. 26.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) 33 (b) 99 (c) 36 (d) 11
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 4 (d) 5
  28. 28.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) 348 (d) 304
  29. 29.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) 153 (c) 54 (d) 51
  30. 30.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 268 (c) 285 (d) 294
  31. 31.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) 216 (b) 24 (c) 72 (d) 75
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  33. 33.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
  34. 34.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 198 (d) 207
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  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) 30 (b) 9 (c) 27 (d) 81
  37. 37.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 562 (c) 446 (d) 561
  38. 38.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 374 (c) 453 (d) 444
  39. 39.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 108 (c) 39 (d) 12
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15

Answer key

  1. 4
  2. 8
  3. 161
  4. 4
  5. 19
  6. 17
  7. 13
  8. 18
  9. 19
  10. 21
  11. 69
  12. 468
  13. 18
  14. 54
  15. 579
  16. 6
  17. 6
  18. 2
  19. 39
  20. 45
  21. 7
  22. 444
  23. 6
  24. 6
  25. 66
  26. 33
  27. 4
  28. 348
  29. 51
  30. 294
  31. 72
  32. 18
  33. 378
  34. 207
  35. 9
  36. 27
  37. 561
  38. 453
  39. 36
  40. 5

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