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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 923 · 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 3? (a) 2 (b) 4 (c) 3 (d) 10
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 17 (d) 8
  4. 4.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) 18 (b) 6 (c) 54 (d) 21
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 17 (d) 7
  6. 6.The numbers 17 to 25 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) 63 (c) 21 (d) 189
  7. 7.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 363 (c) 320 (d) 372
  8. 8.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 102 (c) 101 (d) 92
  9. 9.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 303 (c) 294 (d) 274
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 16 (d) 7
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 14 (b) 15 (c) 13 (d) 3
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 17 (b) 18 (c) 19 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  18. 18.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 163 (d) 172
  19. 19.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) 51 (b) 16 (c) 48 (d) 144
  20. 20.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) 45 (b) 135 (c) 48 (d) 15
  21. 21.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 591 (c) 466 (d) 582
  22. 22.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
  23. 23.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) 57 (b) 171 (c) 19 (d) 60
  24. 24.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 190 (c) 180 (d) 198
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  26. 26.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 360 (c) 312 (d) 361
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 8 (d) 20
  28. 28.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 436 (c) 435 (d) 362
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 5 (d) 17
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 18 (d) 19
  31. 31.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 42 (c) 60 (d) 51
  32. 32.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 318 (d) 328
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 4 (d) 6
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  36. 36.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 349 (d) 348
  37. 37.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 119 (d) 110
  38. 38.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 456 (c) 567 (d) 577
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  40. 40.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) 51 (b) 54 (c) 153 (d) 17

Answer key

  1. 3
  2. 7
  3. 18
  4. 18
  5. 17
  6. 63
  7. 372
  8. 101
  9. 303
  10. 6
  11. 5
  12. 5
  13. 17
  14. 14
  15. 18
  16. 6
  17. 4
  18. 163
  19. 48
  20. 45
  21. 591
  22. 30
  23. 57
  24. 189
  25. 3
  26. 360
  27. 19
  28. 435
  29. 16
  30. 19
  31. 51
  32. 327
  33. 5
  34. 15
  35. 19
  36. 348
  37. 119
  38. 576
  39. 4
  40. 51

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