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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 978 · 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 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) 15 (b) 5 (c) 45 (d) 18
  2. 2.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 588 (d) 597
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 15 (b) 17 (c) 16 (d) 5
  4. 4.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 504 (c) 408 (d) 505
  5. 5.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) 384 (c) 328 (d) 375
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 13 (c) 14 (d) 9
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 16 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 4 (c) 5 (d) 6
  11. 11.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
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 5 (d) 3
  13. 13.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 130 (c) 120 (d) 129
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  15. 15.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 42 (c) 34 (d) 33
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  17. 17.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 550 (c) 438 (d) 540
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  19. 19.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 112 (c) 104 (d) 94
  20. 20.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 474 (d) 394
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 10 (c) 9 (d) 3
  23. 23.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) 216 (b) 75 (c) 72 (d) 24
  24. 24.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) 66 (b) 63 (c) 21 (d) 189
  25. 25.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) 69 (b) 22 (c) 198 (d) 66
  26. 26.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 309 (b) 278 (c) 300 (d) 310
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  28. 28.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) 9 (c) 81 (d) 30
  29. 29.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 238 (c) 237 (d) 230
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 14 (d) 15
  31. 31.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) 48 (b) 16 (c) 144 (d) 51
  32. 32.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 517 (c) 416 (d) 516
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 5 (b) 3 (c) 2 (d) 4
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 6 (b) 4 (c) 7 (d) 5
  35. 35.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) 30 (b) 33 (c) 90 (d) 10
  36. 36.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) 63 (b) 21 (c) 7 (d) 24
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 5 (c) 2 (d) 4
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 15 (d) 13
  40. 40.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7

Answer key

  1. 15
  2. 597
  3. 16
  4. 504
  5. 384
  6. 13
  7. 17
  8. 4
  9. 9
  10. 5
  11. 69
  12. 4
  13. 129
  14. 6
  15. 33
  16. 6
  17. 549
  18. 5
  19. 103
  20. 483
  21. 9
  22. 10
  23. 72
  24. 63
  25. 66
  26. 309
  27. 2
  28. 27
  29. 237
  30. 15
  31. 48
  32. 516
  33. 4
  34. 6
  35. 30
  36. 21
  37. 4
  38. 4
  39. 14
  40. 8

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