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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 748 · 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 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
  2. 2.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) 69 (b) 207 (c) 72 (d) 23
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 6 (d) 4
  5. 5.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 137 (c) 128 (d) 146
  6. 6.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
  7. 7.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) 18 (c) 6 (d) 54
  8. 8.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) 18 (b) 45 (c) 15 (d) 5
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21
  10. 10.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 289 (c) 288 (d) 279
  11. 11.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 52 (c) 62 (d) 61
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  13. 13.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 100 (c) 110 (d) 118
  14. 14.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 286 (d) 322
  15. 15.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) 144 (c) 51 (d) 16
  16. 16.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 396 (d) 397
  17. 17.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 91 (c) 100 (d) 92
  18. 18.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 540 (c) 550 (d) 438
  19. 19.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 52 (d) 60
  20. 20.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
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 15 (d) 3
  22. 22.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 178 (c) 196 (d) 187
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 4 (d) 16
  25. 25.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 253 (c) 252 (d) 243
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 6 (b) 9 (c) 5 (d) 8
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 52? (a) 4 (b) 3 (c) 5 (d) 6
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 4 (d) 3
  29. 29.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 261 (c) 246 (d) 252
  30. 30.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 516 (c) 517 (d) 507
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  34. 34.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 267 (c) 250 (d) 268
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 3 (d) 2
  36. 36.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 136 (c) 154 (d) 145
  37. 37.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 468 (c) 594 (d) 595
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 20 (c) 8 (d) 19
  39. 39.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 15 (d) 14

Answer key

  1. 33
  2. 69
  3. 8
  4. 5
  5. 137
  6. 66
  7. 18
  8. 15
  9. 20
  10. 288
  11. 61
  12. 19
  13. 109
  14. 321
  15. 48
  16. 396
  17. 91
  18. 549
  19. 51
  20. 21
  21. 14
  22. 187
  23. 4
  24. 15
  25. 252
  26. 8
  27. 5
  28. 5
  29. 261
  30. 516
  31. 2
  32. 3
  33. 5
  34. 267
  35. 4
  36. 145
  37. 594
  38. 19
  39. 7
  40. 14

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