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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 851 · 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 8? (a) 8 (b) 10 (c) 9 (d) 7
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 18 (d) 8
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 15 (d) 16
  4. 4.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 355 (c) 308 (d) 354
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  6. 6.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) 21 (b) 54 (c) 18 (d) 6
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  9. 9.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 125 (b) 116 (c) 126 (d) 134
  10. 10.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) 47 (c) 56 (d) 38
  11. 11.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 243 (c) 252 (d) 240
  12. 12.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 273 (c) 274 (d) 254
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  14. 14.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
  15. 15.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 302 (b) 345 (c) 346 (d) 336
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 4 (d) 2
  18. 18.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) 63 (b) 21 (c) 24 (d) 7
  19. 19.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) 22 (b) 69 (c) 198 (d) 66
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  22. 22.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) 54 (b) 153 (c) 51 (d) 17
  23. 23.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) 16 (c) 144 (d) 51
  24. 24.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) 36 (b) 33 (c) 99 (d) 11
  25. 25.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  26. 26.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 374 (c) 453 (d) 444
  27. 27.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 258 (c) 244 (d) 249
  28. 28.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 193 (c) 200 (d) 183
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 6 (b) 8 (c) 7 (d) 5
  30. 30.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 5 (b) 8 (c) 6 (d) 7
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 15 (d) 4
  33. 33.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 198 (c) 208 (d) 210
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 20 (d) 19
  35. 35.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 486 (c) 496 (d) 495
  36. 36.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 327 (c) 328 (d) 290
  37. 37.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 35 (c) 36 (d) 44
  38. 38.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 301 (c) 291 (d) 300
  39. 39.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 20 (d) 19

Answer key

  1. 8
  2. 18
  3. 15
  4. 354
  5. 3
  6. 18
  7. 57
  8. 4
  9. 125
  10. 47
  11. 252
  12. 273
  13. 3
  14. 30
  15. 345
  16. 4
  17. 3
  18. 21
  19. 66
  20. 6
  21. 7
  22. 51
  23. 48
  24. 33
  25. 8
  26. 453
  27. 258
  28. 192
  29. 7
  30. 5
  31. 7
  32. 15
  33. 207
  34. 19
  35. 495
  36. 327
  37. 35
  38. 300
  39. 2
  40. 19

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