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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 603 · 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 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) 16 (b) 48 (c) 51 (d) 144
  2. 2.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
  3. 3.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 38 (c) 47 (d) 56
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 4 (b) 6 (c) 3 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  8. 8.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) 66 (b) 69 (c) 22 (d) 198
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 14 (d) 15
  10. 10.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) 8 (b) 72 (c) 27 (d) 24
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 4 (c) 16 (d) 14
  12. 12.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 304 (c) 339 (d) 348
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 5 (b) 6 (c) 7 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  16. 16.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 256 (c) 277 (d) 267
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 9 (c) 4 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  19. 19.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 507 (c) 517 (d) 516
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  21. 21.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 223 (c) 220 (d) 222
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 16 (d) 4
  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) 75 (b) 24 (c) 72 (d) 216
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 2 (d) 3
  25. 25.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 110 (c) 109 (d) 100
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 18 (b) 16 (c) 6 (d) 17
  27. 27.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 393 (c) 384 (d) 334
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 4 (d) 5
  29. 29.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 273 (c) 264 (d) 254
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 12 (c) 13 (d) 3
  32. 32.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) 17 (b) 153 (c) 54 (d) 51
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 16 (d) 6
  35. 35.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 31 (d) 40
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 18 (b) 20 (c) 19 (d) 9
  37. 37.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
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  39. 39.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 10 (c) 12 (d) 13

Answer key

  1. 48
  2. 30
  3. 47
  4. 2
  5. 5
  6. 9
  7. 16
  8. 66
  9. 14
  10. 24
  11. 15
  12. 348
  13. 7
  14. 8
  15. 6
  16. 276
  17. 8
  18. 5
  19. 516
  20. 3
  21. 222
  22. 15
  23. 72
  24. 4
  25. 109
  26. 17
  27. 393
  28. 4
  29. 273
  30. 5
  31. 13
  32. 51
  33. 7
  34. 17
  35. 31
  36. 19
  37. 15
  38. 4
  39. 3
  40. 12

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