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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 237 · 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 two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  2. 2.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) 15 (c) 135 (d) 45
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 2
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 5 (b) 7 (c) 4 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 12 (b) 4 (c) 11 (d) 13
  10. 10.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) 18 (b) 5 (c) 15 (d) 45
  11. 11.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 53 (d) 62
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  13. 13.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 334 (c) 394 (d) 384
  14. 14.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 226 (c) 222 (d) 232
  15. 15.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 170 (c) 160 (d) 169
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  17. 17.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) 9 (b) 81 (c) 30 (d) 27
  18. 18.The numbers 4 to 12 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) 8 (c) 24 (d) 27
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 16 (b) 18 (c) 17 (d) 7
  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) 436 (b) 547 (c) 546 (d) 537
  21. 21.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 315 (c) 316 (d) 306
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 4 (c) 15 (d) 13
  24. 24.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 96 (c) 104 (d) 95
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 9 (d) 20
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 21 (d) 20
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 13 (d) 14
  32. 32.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 195 (c) 202 (d) 196
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 17 (c) 16 (d) 6
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 18 (d) 20
  36. 36.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 11 (c) 99 (d) 36
  37. 37.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 234 (c) 228 (d) 235
  38. 38.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 369 (c) 370 (d) 318
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 8 (b) 20 (c) 19 (d) 18
  40. 40.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) 57 (b) 162 (c) 18 (d) 54

Answer key

  1. 3
  2. 45
  3. 4
  4. 9
  5. 6
  6. 2
  7. 2
  8. 6
  9. 12
  10. 15
  11. 53
  12. 16
  13. 393
  14. 231
  15. 169
  16. 7
  17. 27
  18. 24
  19. 17
  20. 546
  21. 315
  22. 5
  23. 14
  24. 95
  25. 20
  26. 20
  27. 19
  28. 8
  29. 20
  30. 20
  31. 14
  32. 195
  33. 20
  34. 17
  35. 19
  36. 33
  37. 234
  38. 369
  39. 19
  40. 54

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