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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 150 · 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 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) 10 (b) 30 (c) 33 (d) 90
  2. 2.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) 27 (c) 24 (d) 8
  3. 3.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) 60 (b) 171 (c) 19 (d) 57
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  6. 6.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) 45 (c) 5 (d) 18
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 14 (c) 4 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  9. 9.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
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 12 (c) 11 (d) 10
  11. 11.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 324 (c) 379 (d) 378
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
  13. 13.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 345 (c) 355 (d) 308
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 5 (d) 2
  15. 15.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 258 (c) 280 (d) 270
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 3 (d) 15
  17. 17.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 161 (c) 162 (d) 152
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  19. 19.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 312 (c) 286 (d) 322
  20. 20.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 63 (c) 72 (d) 54
  21. 21.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 107 (c) 108 (d) 116
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 4 (d) 2
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 5 (c) 15 (d) 16
  25. 25.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 637 (c) 636 (d) 627
  26. 26.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 405 (c) 348 (d) 414
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  30. 30.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 474 (c) 475 (d) 388
  31. 31.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) 144 (b) 51 (c) 48 (d) 16
  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) 54 (c) 153 (d) 51
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  35. 35.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
  36. 36.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 478 (d) 600
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 5 (c) 4 (d) 3
  38. 38.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 58 (c) 67 (d) 76
  39. 39.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  40. 40.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) 24 (b) 21 (c) 7 (d) 63

Answer key

  1. 30
  2. 24
  3. 57
  4. 6
  5. 5
  6. 15
  7. 14
  8. 6
  9. 33
  10. 11
  11. 378
  12. 19
  13. 354
  14. 4
  15. 279
  16. 14
  17. 161
  18. 9
  19. 321
  20. 63
  21. 107
  22. 19
  23. 3
  24. 15
  25. 636
  26. 414
  27. 2
  28. 3
  29. 17
  30. 474
  31. 48
  32. 51
  33. 2
  34. 3
  35. 45
  36. 609
  37. 4
  38. 67
  39. 7
  40. 21

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