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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 820 · 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 5? (a) 5 (b) 4 (c) 10 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 3 (c) 14 (d) 15
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 18 (d) 6
  6. 6.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 255 (c) 265 (d) 264
  7. 7.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 228 (c) 234 (d) 235
  8. 8.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) 48 (b) 15 (c) 45 (d) 135
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  10. 10.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 498 (c) 630 (d) 639
  11. 11.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) 8 (d) 27
  12. 12.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) 39 (c) 12 (d) 108
  13. 13.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 256 (c) 267 (d) 276
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
  16. 16.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  17. 17.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 445 (c) 444 (d) 435
  18. 18.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) 162 (c) 57 (d) 18
  19. 19.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 332 (c) 391 (d) 390
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 6 (d) 16
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  22. 22.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) 11 (b) 36 (c) 99 (d) 33
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  24. 24.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 442 (c) 556 (d) 555
  25. 25.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) 295 (c) 285 (d) 294
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 6 (d) 4
  27. 27.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 144 (c) 153 (d) 154
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  29. 29.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 136 (c) 144 (d) 135
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 5 (c) 4 (d) 6
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 3 (d) 2
  32. 32.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 164 (c) 174 (d) 173
  33. 33.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 156 (c) 165 (d) 166
  34. 34.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) 161 (d) 162
  35. 35.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 262 (d) 252
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 6 (d) 17
  37. 37.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) 72 (b) 216 (c) 24 (d) 75
  38. 38.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  39. 39.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 111 (c) 120 (d) 112
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2

Answer key

  1. 5
  2. 9
  3. 14
  4. 6
  5. 17
  6. 264
  7. 234
  8. 45
  9. 5
  10. 639
  11. 24
  12. 36
  13. 276
  14. 6
  15. 19
  16. 7
  17. 444
  18. 54
  19. 390
  20. 17
  21. 5
  22. 33
  23. 3
  24. 555
  25. 294
  26. 6
  27. 153
  28. 8
  29. 135
  30. 6
  31. 4
  32. 173
  33. 165
  34. 161
  35. 261
  36. 17
  37. 72
  38. 2
  39. 111
  40. 3

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