Frank and Grant just bet: were there more odd-numbered or even-numbered presidents on US banknotes up to $100. Jeff happened to know all presidents by their numbers but couldn’t match them with the banknotes. Some cell phones just ran out of batteries, some didn’t have Internet connection. No library worked already.
Jack just recalled there was a unique and unusual ATM nearby. It happened to split the required amount of cash based on how many times a biggest possible banknote could fit in the it. Say, it always dispensed $102 as a $100 and a $2 banknote. Yes, it had $2!
Having only bank cards with them and Frank having just a $10 banknote, the first question appeared for the four friends was: what should be the minimum amount of cash to be asked in the ATM so that to obtain all possible banknotes up to $100?
The minimum cash amount required is the sum of all US banknotes up to $100. It makes $188 in total. Since Frank already had a $10 banknote with him, the $178 was enough to be asked in the ATM.
BTW, there are 3 odd-numbered and 2 even-numbered presidents on US banknotes up to $100: George Washington (1st), Thomas Jefferson (3rd), Andrew Jackson (7th), Abraham Lincoln (16th), and Ulysses S. Grant (18th).