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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 789 · 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.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 57 (c) 60 (d) 19
  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) 180 (c) 20 (d) 63
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 4 (c) 5 (d) 6
  6. 6.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 45 (d) 42
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  8. 8.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 544 (c) 434 (d) 534
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 7 (b) 16 (c) 15 (d) 17
  11. 11.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 231 (c) 241 (d) 232
  12. 12.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 246 (c) 247 (d) 236
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 5 (d) 7
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 3 (d) 15
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  16. 16.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 284 (c) 309 (d) 318
  17. 17.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 32 (c) 31 (d) 22
  18. 18.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 492 (c) 493 (d) 400
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 17 (d) 15
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 7 (b) 4 (c) 6 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 13 (b) 9 (c) 15 (d) 16
  27. 27.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 540 (c) 550 (d) 549
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  29. 29.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) 48 (b) 135 (c) 15 (d) 45
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  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) 66 (c) 21 (d) 63
  32. 32.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) 72 (b) 207 (c) 23 (d) 69
  33. 33.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 212 (c) 201 (d) 211
  34. 34.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 619 (c) 618 (d) 484
  35. 35.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
  36. 36.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 453 (c) 444 (d) 374
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 4 (d) 5
  38. 38.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 507 (c) 516 (d) 517
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  40. 40.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 87 (d) 78

Answer key

  1. 57
  2. 60
  3. 5
  4. 3
  5. 6
  6. 42
  7. 9
  8. 543
  9. 3
  10. 16
  11. 240
  12. 246
  13. 6
  14. 14
  15. 2
  16. 318
  17. 31
  18. 492
  19. 19
  20. 3
  21. 18
  22. 16
  23. 6
  24. 3
  25. 18
  26. 15
  27. 549
  28. 18
  29. 45
  30. 8
  31. 63
  32. 69
  33. 210
  34. 618
  35. 21
  36. 453
  37. 5
  38. 516
  39. 4
  40. 87

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