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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 39 · 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) 8 (b) 7 (c) 10 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 17 (b) 15 (c) 16 (d) 5
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 15 (d) 3
  7. 7.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 409 (c) 344 (d) 408
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 18
  9. 9.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 348 (c) 349 (d) 339
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 17 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  12. 12.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 264 (c) 265 (d) 248
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 15 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  15. 15.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) 18 (b) 15 (c) 45 (d) 5
  16. 16.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) 51 (b) 144 (c) 16 (d) 48
  17. 17.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) 162 (b) 54 (c) 18 (d) 57
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  20. 20.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) 54 (b) 18 (c) 6 (d) 21
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  22. 22.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) 117 (b) 13 (c) 39 (d) 42
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 19 (d) 20
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 579 (c) 588 (d) 464
  26. 26.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 218 (c) 220 (d) 210
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 2 (b) 3 (c) 5 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  29. 29.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 573 (c) 460 (d) 582
  30. 30.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
  31. 31.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
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  33. 33.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) 45 (b) 42 (c) 126 (d) 14
  34. 34.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 366 (c) 432 (d) 441
  35. 35.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) 290 (c) 327 (d) 318
  36. 36.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 130 (d) 129
  37. 37.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) 15 (b) 135 (c) 45 (d) 48
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 20 (b) 18 (c) 8 (d) 19
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7

Answer key

  1. 7
  2. 6
  3. 8
  4. 16
  5. 16
  6. 14
  7. 408
  8. 17
  9. 348
  10. 17
  11. 6
  12. 264
  13. 16
  14. 5
  15. 15
  16. 48
  17. 54
  18. 19
  19. 5
  20. 18
  21. 7
  22. 39
  23. 19
  24. 4
  25. 588
  26. 219
  27. 4
  28. 3
  29. 582
  30. 72
  31. 21
  32. 4
  33. 42
  34. 441
  35. 327
  36. 129
  37. 45
  38. 4
  39. 19
  40. 8

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