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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 989 · 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 4 written when you write all the numbers from 1 to 40? (a) 6 (b) 5 (c) 3 (d) 4
  2. 2.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 51 (b) 52 (c) 42 (d) 60
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 3 (d) 4
  4. 4.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 280 (d) 303
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 5 (c) 3 (d) 4
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 15 (d) 13
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 6 (b) 7 (c) 4 (d) 5
  11. 11.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 28 (d) 46
  12. 12.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 496 (c) 495 (d) 486
  13. 13.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) 612 (d) 603
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  15. 15.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 258 (c) 267 (d) 268
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 3 (d) 2
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  18. 18.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 126 (c) 108 (d) 117
  19. 19.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) 24 (b) 72 (c) 27 (d) 8
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 8 (b) 7 (c) 6 (d) 9
  21. 21.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 156 (c) 148 (d) 147
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 3 (d) 2
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 5 (c) 4 (d) 2
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 8 (d) 17
  25. 25.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) 75 (c) 24 (d) 72
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 17 (d) 5
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  29. 29.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 21
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  33. 33.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 372 (c) 441 (d) 450
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  35. 35.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 294 (c) 285 (d) 295
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 17 (d) 16
  39. 39.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 421 (c) 352 (d) 420
  40. 40.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) 198 (b) 69 (c) 66 (d) 22

Answer key

  1. 5
  2. 51
  3. 4
  4. 312
  5. 2
  6. 3
  7. 19
  8. 5
  9. 14
  10. 6
  11. 37
  12. 495
  13. 612
  14. 4
  15. 267
  16. 4
  17. 3
  18. 117
  19. 24
  20. 8
  21. 147
  22. 4
  23. 4
  24. 18
  25. 72
  26. 9
  27. 16
  28. 6
  29. 8
  30. 20
  31. 5
  32. 4
  33. 450
  34. 7
  35. 294
  36. 3
  37. 9
  38. 16
  39. 420
  40. 66

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