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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 689 · 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 1 written when you write all the numbers from 1 to 51? (a) 15 (b) 17 (c) 16 (d) 5
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 8 (b) 7 (c) 9 (d) 6
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 2 (d) 1
  6. 6.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 303 (d) 274
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 18
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 18 (d) 19
  9. 9.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 258 (c) 267 (d) 250
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 3 (d) 5
  11. 11.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) 5 (b) 18 (c) 45 (d) 15
  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) 265 (b) 255 (c) 264 (d) 248
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 3 (d) 14
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  15. 15.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 71 (d) 62
  16. 16.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 30 (d) 81
  17. 17.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 207 (c) 210 (d) 208
  18. 18.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 240 (c) 253 (d) 243
  19. 19.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 459 (c) 468 (d) 384
  20. 20.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) 24 (b) 75 (c) 216 (d) 72
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  24. 24.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) 6 (c) 21 (d) 54
  25. 25.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 70 (c) 80 (d) 88
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 17 (d) 16
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 2 (d) 3
  28. 28.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 544 (c) 434 (d) 543
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 19 (d) 20
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  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) 189 (b) 63 (c) 21 (d) 66
  32. 32.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 231 (c) 226 (d) 232
  33. 33.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 3 (d) 4
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  36. 36.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) 69 (b) 198 (c) 22 (d) 66
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 18 (d) 7
  38. 38.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 458 (c) 580 (d) 579
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 6 (d) 5
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6

Answer key

  1. 16
  2. 15
  3. 5
  4. 8
  5. 3
  6. 303
  7. 17
  8. 18
  9. 267
  10. 5
  11. 15
  12. 264
  13. 14
  14. 5
  15. 71
  16. 27
  17. 207
  18. 252
  19. 468
  20. 72
  21. 7
  22. 9
  23. 3
  24. 18
  25. 79
  26. 17
  27. 4
  28. 543
  29. 20
  30. 3
  31. 63
  32. 231
  33. 8
  34. 3
  35. 4
  36. 66
  37. 17
  38. 579
  39. 5
  40. 5

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