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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 113 · 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 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) 20 (b) 60 (c) 63 (d) 180
  2. 2.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 242 (c) 246 (d) 256
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 5 (b) 6 (c) 3 (d) 4
  5. 5.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 573 (c) 582 (d) 460
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 19 (d) 21
  8. 8.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 94 (d) 85
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 5 (d) 2
  10. 10.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) 99 (b) 36 (c) 11 (d) 33
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 3 (c) 4 (d) 2
  13. 13.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 160 (c) 152 (d) 151
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 7 (c) 8 (d) 5
  16. 16.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 107 (d) 108
  17. 17.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) 24 (b) 72 (c) 8 (d) 27
  18. 18.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) 13 (b) 39 (c) 42 (d) 117
  19. 19.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 276 (c) 306 (d) 297
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  21. 21.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) 7 (b) 21 (c) 24 (d) 63
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 4 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  24. 24.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 44 (c) 43 (d) 34
  25. 25.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) 33 (b) 10 (c) 90 (d) 30
  26. 26.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 262 (c) 252 (d) 246
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 5 (b) 8 (c) 7 (d) 6
  28. 28.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 333 (c) 294 (d) 324
  29. 29.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 315 (c) 325 (d) 324
  30. 30.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 207 (c) 208 (d) 210
  31. 31.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  33. 33.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 207 (c) 324 (d) 216
  34. 34.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 276 (c) 277 (d) 267
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 16 (d) 4
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 5 (c) 15 (d) 17
  37. 37.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 268 (c) 258 (d) 267
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4

Answer key

  1. 60
  2. 255
  3. 2
  4. 5
  5. 582
  6. 3
  7. 20
  8. 85
  9. 4
  10. 33
  11. 9
  12. 4
  13. 151
  14. 5
  15. 7
  16. 107
  17. 24
  18. 39
  19. 306
  20. 8
  21. 21
  22. 4
  23. 2
  24. 43
  25. 30
  26. 261
  27. 7
  28. 333
  29. 324
  30. 207
  31. 7
  32. 6
  33. 216
  34. 276
  35. 15
  36. 16
  37. 267
  38. 19
  39. 4
  40. 3

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