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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 122 · 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.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 196 (c) 202 (d) 186
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 17 (c) 5 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 9 (b) 11 (c) 12 (d) 8
  5. 5.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 50 (c) 60 (d) 68
  6. 6.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) 10 (c) 33 (d) 30
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 14 (c) 3 (d) 13
  9. 9.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) 45 (d) 15
  10. 10.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) 51 (c) 16 (d) 144
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  12. 12.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) 19 (c) 60 (d) 57
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 7 (c) 3 (d) 4
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  16. 16.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) 24 (d) 63
  17. 17.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 190 (c) 189 (d) 198
  18. 18.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
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 18 (d) 17
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 6 (b) 4 (c) 5 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  23. 23.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) 180 (b) 60 (c) 20 (d) 63
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  25. 25.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 338 (c) 399 (d) 400
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 16 (d) 4
  27. 27.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 219 (c) 224 (d) 228
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 15 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 18 (b) 19 (c) 17 (d) 7
  33. 33.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 322 (c) 376 (d) 375
  34. 34.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) 126 (b) 45 (c) 42 (d) 14
  35. 35.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 582 (d) 466
  36. 36.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 528 (c) 529 (d) 519
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 4 (c) 10 (d) 11
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 14 (d) 4
  39. 39.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 80 (c) 70 (d) 79
  40. 40.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 207 (c) 208 (d) 198

Answer key

  1. 195
  2. 16
  3. 7
  4. 11
  5. 59
  6. 30
  7. 6
  8. 14
  9. 45
  10. 48
  11. 3
  12. 57
  13. 8
  14. 6
  15. 19
  16. 21
  17. 189
  18. 6
  19. 18
  20. 2
  21. 5
  22. 3
  23. 60
  24. 9
  25. 399
  26. 15
  27. 228
  28. 15
  29. 4
  30. 7
  31. 5
  32. 18
  33. 375
  34. 42
  35. 591
  36. 528
  37. 10
  38. 14
  39. 79
  40. 207

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