I appear in the morning but am always there.
You can never see me though I am everywhere.
By night I am gone, though I sometimes never was.
Nothing can defeat me but I am easily gone.
Chuck and Ruby were going to meet at a hotel for their anniversary dinner, but Ruby didn’t show. Chuck was angry and left her a passive aggressive message on their kitchen table in the form of fifteen matchsticks spelling “hotel” and went to bed. When Ruby got home and saw the matchsticks, she removed one and went to bed. When Chuck woke up the next morning and saw Ruby’s new message, he realized his mistake. Which stick did Ruby remove and what was the new message?
Ruby had removed the top of the T and the new message could be seen upside down from where Chuck sat at his breakfast of sadness and anger. What he saw was 7 3 1 0 4, or 7/31/04, the date of their anniversary. In his excitement, Chuck had gone to the restaurant a day early, on July 30th. All was forgiven by both parties and Chuck and Ruby had a wonderful dinner together. They also promised to buy a whiteboard for the kitchen so they wouldn’t have to use matchstick messages ever again.
Alfred is at the bank to cash his $200 check. He tells the cashier he would like some one dollar bills, ten times as many two dollar bills and the rest in fives.
How many of each denomination does the cashier need to give Alfred?
We know that in order to give the rest of the amount in fives, the sum of the one and two dollar bills needs to be divisible by five (i.e. end in 0 or 5).
If we start with a single one dollar bill, we’d need ten two dollar bills to satisfy the request, making $21. But we need a sum that is divisible by 5. So we keep going up, like so:
Find a six-digit number containing no zeros and no repeated digits that satisfies the following conditions:
1. The first and fourth digits sum to the last digit, as do the third and fifth digits.
2. The first and second digits when read as a two-digit number equal one quarter the fourth and fifth digits.
3. The last digit is four times the third digit.
If you call the number ABCDEF, then you get the following equations.
1. A + D = F and C + E = F
2. AB = DE / 4
3. F = 4 × C
The only numbers that work for C and E are 2 and 6 or 4 and 8, and in order to make F a single-digit number, we can deduce that C = 2, E = 6 and F = 8.
So far, our number is AB2D68.
We know A + D = 8 so A and D are both odd numbers. The only odd number less than 8 that we can use for D to make one-quarter of two-digit number D6 also be a two-digit number is 7, so D = 7 and A is 1. This makes the two-digit number AB 19.
