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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 430 · 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 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 62 (c) 71 (d) 72
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 21 (b) 20 (c) 9 (d) 19
  3. 3.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 128 (c) 127 (d) 136
  4. 4.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 36 (c) 35 (d) 26
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  6. 6.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 591 (c) 601 (d) 600
  7. 7.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 642 (c) 500 (d) 643
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
  10. 10.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 240 (d) 241
  11. 11.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 48 (c) 16 (d) 51
  12. 12.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 142 (c) 151 (d) 160
  13. 13.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 132 (c) 124 (d) 114
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  15. 15.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) 6 (b) 18 (c) 54 (d) 21
  16. 16.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) 448 (d) 555
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 7 (c) 8 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  20. 20.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 315 (c) 325 (d) 324
  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) 286 (b) 312 (c) 322 (d) 321
  22. 22.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 300 (d) 301
  23. 23.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 603 (d) 612
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 3 (d) 14
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 18 (d) 7
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 7 (b) 10 (c) 8 (d) 9
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 5 (c) 3 (d) 6
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 6 (d) 16
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  32. 32.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) 15 (c) 45 (d) 18
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 8 (d) 20
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 17 (b) 16 (c) 18 (d) 7
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 5 (d) 6
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  38. 38.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 243 (c) 252 (d) 253
  39. 39.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 217 (c) 207 (d) 324
  40. 40.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) 153 (c) 144 (d) 154

Answer key

  1. 71
  2. 20
  3. 127
  4. 35
  5. 4
  6. 600
  7. 642
  8. 7
  9. 20
  10. 240
  11. 48
  12. 151
  13. 123
  14. 2
  15. 18
  16. 564
  17. 15
  18. 8
  19. 2
  20. 324
  21. 321
  22. 300
  23. 612
  24. 14
  25. 18
  26. 9
  27. 5
  28. 18
  29. 17
  30. 6
  31. 8
  32. 15
  33. 3
  34. 19
  35. 17
  36. 5
  37. 4
  38. 252
  39. 216
  40. 153

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