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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 77 · 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 7 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 19 (d) 20
  2. 2.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 180 (d) 20
  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) 9 (d) 30
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 18 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  7. 7.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) 22 (c) 69 (d) 66
  8. 8.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 66 (c) 74 (d) 56
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 6 (d) 4
  10. 10.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 340 (c) 330 (d) 339
  11. 11.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) 135 (b) 15 (c) 48 (d) 45
  12. 12.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 100 (c) 92 (d) 91
  13. 13.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 310 (d) 309
  14. 14.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 331 (c) 292 (d) 321
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  17. 17.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) 72 (b) 8 (c) 27 (d) 24
  18. 18.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 601 (d) 600
  19. 19.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 264 (c) 279 (d) 288
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 17 (d) 16
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 5 (c) 15 (d) 14
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  24. 24.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 498 (c) 640 (d) 639
  25. 25.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) 45 (c) 15 (d) 5
  26. 26.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 39 (c) 12 (d) 108
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 4 (d) 16
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 18 (d) 17
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  30. 30.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) 10 (b) 90 (c) 30 (d) 33
  31. 31.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
  32. 32.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 258 (c) 268 (d) 267
  33. 33.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 324 (d) 288
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 13 (c) 15 (d) 8
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  38. 38.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
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
  40. 40.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 156 (d) 138

Answer key

  1. 19
  2. 60
  3. 27
  4. 19
  5. 18
  6. 9
  7. 66
  8. 65
  9. 5
  10. 339
  11. 45
  12. 91
  13. 309
  14. 330
  15. 5
  16. 7
  17. 24
  18. 600
  19. 288
  20. 16
  21. 15
  22. 2
  23. 4
  24. 639
  25. 15
  26. 36
  27. 15
  28. 17
  29. 5
  30. 30
  31. 432
  32. 267
  33. 324
  34. 15
  35. 4
  36. 6
  37. 3
  38. 21
  39. 3
  40. 147

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