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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 360 · 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 5 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  3. 3.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) 27 (b) 81 (c) 30 (d) 9
  4. 4.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 140 (d) 149
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 5 (d) 14
  7. 7.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 543 (d) 534
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 2 (d) 3
  9. 9.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) 54 (c) 21 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  13. 13.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 612 (c) 613 (d) 480
  14. 14.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) 16 (c) 48 (d) 51
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 16 (b) 5 (c) 14 (d) 15
  17. 17.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 313 (c) 312 (d) 303
  18. 18.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 160 (c) 169 (d) 170
  19. 19.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 297 (c) 307 (d) 276
  20. 20.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 252 (c) 240 (d) 243
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 7 (d) 19
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  25. 25.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) 75 (c) 216 (d) 24
  26. 26.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) 24 (b) 63 (c) 7 (d) 21
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 5 (b) 15 (c) 14 (d) 16
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 7 (b) 6 (c) 8 (d) 5
  29. 29.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 210 (c) 212 (d) 211
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  31. 31.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 88 (c) 106 (d) 98
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 7 (b) 6 (c) 8 (d) 5
  33. 33.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 68 (c) 50 (d) 59
  34. 34.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 519 (c) 418 (d) 510
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 17 (c) 15 (d) 16
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 9 (d) 20
  37. 37.The numbers 19 to 27 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) 23 (c) 207 (d) 72
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 9 (d) 18
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 5 (d) 3
  40. 40.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58

Answer key

  1. 4
  2. 5
  3. 27
  4. 149
  5. 3
  6. 15
  7. 543
  8. 3
  9. 18
  10. 4
  11. 8
  12. 2
  13. 612
  14. 48
  15. 16
  16. 15
  17. 312
  18. 169
  19. 306
  20. 252
  21. 7
  22. 18
  23. 19
  24. 2
  25. 72
  26. 21
  27. 15
  28. 7
  29. 210
  30. 3
  31. 97
  32. 7
  33. 59
  34. 519
  35. 16
  36. 19
  37. 69
  38. 19
  39. 5
  40. 57

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