It was lunchtime on one of those hot cloudless days that occasionally afflict this side of the country this time of year (it was the fifth Friday in July). I had already settled down, with my ice-cream, in the middle of a bench at one of the picnic tables on the edge of the park, waiting for Megan, when I saw her come from the Kalorie Kram across the street, bearing lunch. She didn't climb into the middle of the bench opposite -- tricky, perhaps, in that calf-length pencil skirt -- but perched on the end.
"Gosh, I'm glad to be out of that stuffy office", she began. She has a part-time job at the tile shop. It's a small business run by Messrs. Fish & Repp -- the name's confused some customers, she tells me. A few munches later, she went on. "Curious thing happened recently, with a couple of our online orders. Did I tell you, we've started selling some of our tiles online? The customer selects the sort of tiles and types the number of tiles into the web page. Now some sorts of tile come in packs. So we work out how to make up the number the customer ordered, in packs. Then Simon out the back of our shop puts the packs into parcels for posting. We don't charge separately for postage, we just mark up the price per tile."
"Ah -- Simon's problem is how to find room to fit the packs into the parcels. So how big..."
"No, that's not the problem -- it's more the weight. You see, with the courier we use, we mustn't pack more than 25kg into a parcel. Anyway, yesterday, we got an online order for white ceramic tiles. That sort come in packs of 7 and 11, and the packs weigh 7kg and 11kg."
"What strange numbers."
"Yeah -- dunno why they package them like that. Still, it means that so long as the order's big enough we can make up the exact number the customer ordered. If it's a small order like 16 or something, then we have to split a pack, but we avoid that if possible. So Simon said Good job that order isn't too big -- we've only got 20 packs of 'em in stock. But that's more than enough for that order."
"OK, with you so far."
"But here's the funny thing. This morning, another online order. Same sort of tiles, five tiles more. We still had enough of them in stock, but this time Simon managed to pack 'em into one parcel less than that other time. Boss was giving him grief over how come he needed one parcel more with that other order, and do you know how much the postal charges are..."
So, how many tiles were in each of those orders, and how many parcels were used for each?