Answer
If the sum of the digits is divisible by nine, so is the number.
Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.
For example, is 486451464 divisible by 9?
Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.
Is 42 divisible by 9? Not sure, you can then do:
4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.
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Puzzle 2
Four friends were discussing the colours of the flowers they had for the local flower show, from this year, and last.
There were four different colours: red, green, blue and yellow.
No-one entered the same colour flower twice. The entrant who currently has the green flowers, used to have yellow. Betty, who is not Mrs Long, currently has the blue flowers. Mrs Kipper, who now has yellow flowers, used to have blue. Neither Mrs Annie Ford, nor Mrs Jester, have ever owned yellow flowers. Cybil is not Mrs Kipper. Diane and Annie have entered four different colours in total.
Can you determine the full names, and colours of the flowers the ladies currently have, and previously had?
Hint
Start with Betty, Mrs Kipper, and Ada, as these are three different people.
Answer
Now Last
Annie Ford Red Green
Betty Jester Blue Red
Cybil Long Green Yellow
Diane Kipper Yellow Blue
Reasoning
By (3), Betty currently has Blue flowers.
Now Last
Betty Blue
By (4), Mrs Kipper currently has Yellow flowers, and used to have Blue.
Now Last
Betty Blue
Kipper Yellow Blue
By (5), we know Annie Ford's name.
Now Last
Betty Blue
Kipper Yellow Blue
Annie Ford
By (6), Mrs Kipper must be Diane, and the remaining person's name is Cybil.
Now Last
Betty Blue
Diane Kipper Yellow Blue
Annie Ford
Cybil
By (2), whoever currently has the Green flowers used to have Yellow, but by (5) this can't be Annie Ford, so this must be Cybil. Which means that Annie must currently have the Red flowers.
Now Last
Betty Blue
Diane Kipper Yellow Blue
Annie Ford Red
Cybil Green Yellow
By (3), Betty isn't Mrs Long, so must be Mrs Jester. Therefore Cybil must be Mrs Long.
Now Last
Betty Jester Blue
Diane Kipper Yellow Blue
Annie Ford Red
Cybil Long Green Yellow
By (1), Annie Ford must have previously had Green, and Betty Jester had Red.
Now Last
Betty Jester Blue Red
Diane Kipper Yellow Blue
Annie Ford Red Green
Cybil Long Green Yellow
