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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 476 · 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 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 396 (c) 387 (d) 397
  2. 2.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 167 (d) 168
  3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 90 (c) 30 (d) 10
  4. 4.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) 462 (d) 386
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 6 (d) 5
  6. 6.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 176 (c) 186 (d) 194
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 20 (d) 18
  10. 10.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 354 (c) 355 (d) 345
  11. 11.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 168 (c) 178 (d) 177
  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) 248 (b) 264 (c) 255 (d) 265
  13. 13.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) 99 (b) 33 (c) 11 (d) 36
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 7 (b) 6 (c) 4 (d) 5
  16. 16.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 61 (c) 62 (d) 70
  17. 17.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) 21 (c) 189 (d) 66
  18. 18.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 230 (c) 237 (d) 238
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
  20. 20.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 126 (c) 118 (d) 117
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 15 (d) 3
  23. 23.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 402 (c) 495 (d) 486
  24. 24.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 204 (c) 195 (d) 208
  25. 25.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 13 (d) 42
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 14 (c) 3 (d) 13
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 18 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  31. 31.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 166 (c) 158 (d) 148
  32. 32.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 606 (c) 597 (d) 607
  33. 33.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
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 5 (b) 3 (c) 6 (d) 4
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 19 (b) 16 (c) 9 (d) 18
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  37. 37.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 128 (c) 138 (d) 146
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 21
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 6 (c) 7 (d) 5
  40. 40.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) 18 (b) 15 (c) 45 (d) 5

Answer key

  1. 396
  2. 167
  3. 30
  4. 471
  5. 6
  6. 185
  7. 2
  8. 3
  9. 19
  10. 354
  11. 177
  12. 264
  13. 33
  14. 6
  15. 6
  16. 61
  17. 63
  18. 237
  19. 16
  20. 117
  21. 17
  22. 14
  23. 495
  24. 204
  25. 39
  26. 14
  27. 18
  28. 2
  29. 4
  30. 6
  31. 157
  32. 606
  33. 21
  34. 5
  35. 18
  36. 7
  37. 137
  38. 20
  39. 7
  40. 15

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