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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 507 · 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 15? (a) 5 (b) 4 (c) 3 (d) 16
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  3. 3.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) 7 (c) 63 (d) 21
  4. 4.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 378 (c) 379 (d) 369
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 12 (c) 10 (d) 11
  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) 5 (c) 45 (d) 18
  7. 7.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 58 (d) 49
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
  9. 9.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 122 (c) 132 (d) 140
  10. 10.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) 117 (b) 13 (c) 42 (d) 39
  11. 11.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 390 (c) 381 (d) 391
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 4 (d) 5
  14. 14.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) 69 (b) 198 (c) 22 (d) 66
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  16. 16.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 201 (c) 192 (d) 202
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
  18. 18.The numbers 8 to 16 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) 108 (c) 39 (d) 12
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 20 (d) 19
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 6 (d) 18
  21. 21.The numbers 14 to 22 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) 162 (c) 18 (d) 54
  22. 22.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) 33 (d) 11
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  25. 25.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 188 (c) 178 (d) 187
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 5 (b) 7 (c) 4 (d) 6
  27. 27.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 636 (b) 496 (c) 627 (d) 637
  28. 28.The numbers 19 to 27 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) 207 (c) 23 (d) 69
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 20 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  31. 31.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 409 (c) 408 (d) 399
  32. 32.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) 63 (b) 20 (c) 60 (d) 180
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  34. 34.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 546 (d) 537
  35. 35.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 231 (d) 232
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  37. 37.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 433 (c) 423 (d) 360
  38. 38.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) 48 (c) 51 (d) 16
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 5 (d) 2
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6

Answer key

  1. 4
  2. 4
  3. 21
  4. 378
  5. 11
  6. 15
  7. 49
  8. 3
  9. 131
  10. 39
  11. 390
  12. 7
  13. 6
  14. 66
  15. 3
  16. 201
  17. 17
  18. 36
  19. 19
  20. 17
  21. 54
  22. 33
  23. 2
  24. 6
  25. 187
  26. 6
  27. 636
  28. 69
  29. 19
  30. 2
  31. 408
  32. 60
  33. 5
  34. 546
  35. 231
  36. 3
  37. 432
  38. 48
  39. 4
  40. 7

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