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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 966 · 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 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 166 (c) 158 (d) 157
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 2 (c) 3 (d) 5
  4. 4.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 139 (d) 148
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 16 (c) 15 (d) 14
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  8. 8.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 463 (c) 380 (d) 462
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 3 (d) 1
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 9 (c) 21 (d) 20
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 6 (d) 18
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 4 (b) 6 (c) 5 (d) 3
  16. 16.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 34 (c) 43 (d) 44
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
  18. 18.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 146 (c) 137 (d) 128
  19. 19.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 185 (c) 186 (d) 176
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 16 (d) 15
  21. 21.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 6 (d) 3
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
  24. 24.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 471 (c) 386 (d) 462
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 18 (b) 17 (c) 7 (d) 19
  28. 28.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) 108 (b) 12 (c) 39 (d) 36
  29. 29.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 392 (c) 481 (d) 480
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 4 (b) 5 (c) 7 (d) 6
  31. 31.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) 63 (b) 189 (c) 21 (d) 66
  32. 32.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 429 (d) 430
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  34. 34.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) 54 (c) 21 (d) 6
  35. 35.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 138 (c) 130 (d) 120
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 6 (c) 9 (d) 7
  37. 37.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) 7 (b) 24 (c) 63 (d) 21
  38. 38.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 115 (c) 106 (d) 124
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 5 (b) 4 (c) 7 (d) 6
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6

Answer key

  1. 157
  2. 9
  3. 4
  4. 139
  5. 15
  6. 4
  7. 4
  8. 462
  9. 3
  10. 3
  11. 7
  12. 20
  13. 5
  14. 17
  15. 5
  16. 43
  17. 3
  18. 137
  19. 185
  20. 16
  21. 432
  22. 5
  23. 3
  24. 471
  25. 18
  26. 5
  27. 18
  28. 36
  29. 480
  30. 6
  31. 63
  32. 429
  33. 2
  34. 18
  35. 129
  36. 8
  37. 21
  38. 115
  39. 6
  40. 7

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