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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 466 · 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 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) 21 (b) 7 (c) 63 (d) 24
  2. 2.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 362 (c) 435 (d) 426
  3. 3.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) 22 (b) 198 (c) 69 (d) 66
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 9 (d) 19
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 14 (c) 13 (d) 11
  6. 6.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) 18 (d) 45
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 7 (c) 6 (d) 4
  8. 8.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) 19 (b) 60 (c) 57 (d) 171
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  11. 11.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 57 (c) 18 (d) 162
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 7 (b) 5 (c) 4 (d) 6
  14. 14.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) 90 (b) 30 (c) 10 (d) 33
  15. 15.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) 39 (b) 12 (c) 36 (d) 108
  16. 16.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) 20 (b) 63 (c) 180 (d) 60
  17. 17.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 144 (c) 134 (d) 152
  18. 18.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) 18 (b) 6 (c) 21 (d) 54
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 16 (d) 6
  20. 20.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 546 (c) 436 (d) 537
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 17 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 3 (d) 1
  24. 24.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 51 (c) 153 (d) 17
  25. 25.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 166 (c) 165 (d) 174
  26. 26.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 265 (c) 255 (d) 248
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15
  28. 28.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 70 (c) 80 (d) 88
  29. 29.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 320 (c) 363 (d) 373
  30. 30.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 282 (c) 316 (d) 315
  31. 31.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) 42 (c) 45 (d) 126
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  36. 36.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 616 (c) 482 (d) 606
  37. 37.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 375 (c) 384 (d) 328
  38. 38.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 582 (c) 592 (d) 591
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 9 (d) 20
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7

Answer key

  1. 21
  2. 435
  3. 66
  4. 20
  5. 13
  6. 15
  7. 6
  8. 57
  9. 5
  10. 4
  11. 54
  12. 2
  13. 6
  14. 30
  15. 36
  16. 60
  17. 143
  18. 18
  19. 16
  20. 546
  21. 18
  22. 4
  23. 3
  24. 51
  25. 165
  26. 264
  27. 15
  28. 79
  29. 372
  30. 315
  31. 42
  32. 6
  33. 9
  34. 8
  35. 3
  36. 615
  37. 384
  38. 591
  39. 19
  40. 7

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