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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 15 · 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 3 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 7 (d) 18
  2. 2.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 262 (c) 246 (d) 261
  3. 3.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
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 18 (c) 8 (d) 19
  5. 5.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 150 (c) 159 (d) 168
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 5 (d) 14
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  8. 8.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) 75 (b) 72 (c) 24 (d) 216
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 17 (b) 19 (c) 7 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  13. 13.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) 433 (c) 360 (d) 432
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 15 (b) 17 (c) 5 (d) 16
  15. 15.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 117 (c) 13 (d) 39
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 4 (d) 6
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 20 (d) 18
  18. 18.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) 224 (c) 219 (d) 228
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 14 (d) 16
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 4 (d) 5
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  22. 22.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 303 (c) 313 (d) 280
  23. 23.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
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 4 (d) 14
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  26. 26.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) 540 (c) 550 (d) 438
  27. 27.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 552 (c) 562 (d) 446
  28. 28.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 126 (c) 118 (d) 117
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 16 (d) 4
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  32. 32.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) 81 (b) 30 (c) 27 (d) 9
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 17 (d) 7
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 1
  37. 37.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 451 (c) 441 (d) 450
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  39. 39.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) 6 (b) 54 (c) 18 (d) 21
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

  1. 18
  2. 261
  3. 57
  4. 18
  5. 159
  6. 6
  7. 3
  8. 72
  9. 3
  10. 8
  11. 18
  12. 7
  13. 432
  14. 16
  15. 39
  16. 6
  17. 19
  18. 228
  19. 15
  20. 4
  21. 19
  22. 312
  23. 516
  24. 15
  25. 4
  26. 549
  27. 561
  28. 117
  29. 4
  30. 15
  31. 17
  32. 27
  33. 7
  34. 18
  35. 8
  36. 3
  37. 450
  38. 2
  39. 18
  40. 4

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