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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 884 · 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 6? (a) 6 (b) 5 (c) 10 (d) 7
  2. 2.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 249 (d) 238
  3. 3.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) 6 (d) 18
  4. 4.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) 20 (b) 60 (c) 180 (d) 63
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 2 (d) 4
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 11 (b) 8 (c) 9 (d) 10
  7. 7.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) 66 (c) 69 (d) 198
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 5 (d) 4
  9. 9.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 170 (c) 161 (d) 152
  10. 10.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 144 (c) 126 (d) 135
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 5 (b) 7 (c) 6 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  13. 13.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) 12 (c) 108 (d) 39
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 3 (c) 10 (d) 9
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 15 (d) 14
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  18. 18.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 351 (c) 234 (d) 243
  19. 19.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) 372 (c) 363 (d) 320
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  21. 21.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 342 (c) 343 (d) 300
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  23. 23.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) 567 (c) 456 (d) 577
  24. 24.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 62 (d) 53
  25. 25.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 75 (d) 24
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 3 (d) 1
  27. 27.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 64 (c) 55 (d) 46
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 20 (b) 21 (c) 19 (d) 9
  31. 31.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  32. 32.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 80 (c) 89 (d) 98
  33. 33.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) 24 (b) 8 (c) 72 (d) 27
  34. 34.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
  35. 35.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 19 (d) 21
  37. 37.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 310 (c) 309 (d) 278
  38. 38.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 387 (c) 388 (d) 378
  39. 39.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 303 (c) 312 (d) 313
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 19 (b) 18 (c) 8 (d) 20

Answer key

  1. 6
  2. 249
  3. 18
  4. 60
  5. 4
  6. 10
  7. 66
  8. 4
  9. 161
  10. 135
  11. 7
  12. 5
  13. 36
  14. 10
  15. 15
  16. 48
  17. 9
  18. 243
  19. 372
  20. 4
  21. 342
  22. 5
  23. 576
  24. 53
  25. 72
  26. 3
  27. 55
  28. 19
  29. 8
  30. 20
  31. 3
  32. 89
  33. 24
  34. 327
  35. 6
  36. 20
  37. 309
  38. 387
  39. 312
  40. 19

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