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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 12 · 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 6? (a) 5 (b) 10 (c) 6 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 17 (c) 6 (d) 18
  5. 5.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 258 (d) 270
  6. 6.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) 27 (b) 72 (c) 8 (d) 24
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  9. 9.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 302 (d) 346
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 9 (c) 7 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  13. 13.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 388 (c) 387 (d) 330
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 17 (d) 6
  15. 15.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 283 (c) 282 (d) 273
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 5 (d) 2
  18. 18.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 22 (c) 31 (d) 32
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  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) 15 (d) 48
  21. 21.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 286 (c) 312 (d) 321
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  24. 24.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 234 (c) 225 (d) 228
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 3 (b) 13 (c) 15 (d) 14
  26. 26.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 564 (c) 555 (d) 448
  27. 27.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 175 (b) 166 (c) 176 (d) 184
  28. 28.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 412 (c) 346 (d) 402
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 6 (d) 5
  30. 30.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) 21 (b) 54 (c) 6 (d) 18
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 4 (d) 7
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 19 (d) 20
  33. 33.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 460 (d) 582
  34. 34.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
  35. 35.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 193 (c) 192 (d) 183
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
  37. 37.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
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  39. 39.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) 66 (c) 69 (d) 22
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 20 (d) 19

Answer key

  1. 6
  2. 7
  3. 6
  4. 17
  5. 279
  6. 24
  7. 20
  8. 5
  9. 345
  10. 2
  11. 8
  12. 7
  13. 387
  14. 17
  15. 282
  16. 19
  17. 4
  18. 31
  19. 19
  20. 45
  21. 321
  22. 4
  23. 8
  24. 234
  25. 14
  26. 564
  27. 175
  28. 411
  29. 6
  30. 18
  31. 6
  32. 19
  33. 582
  34. 72
  35. 192
  36. 4
  37. 54
  38. 2
  39. 66
  40. 19

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